TheCalculator -new version

[RuiLoureiro]

Hi
        Here is TheCalculator v2017.01- first version.
        It is possible that we may find some bugs: all things that i did was new things to me.
       
        Derivatives are done following a new complete method that i created:
        we analyse the expression and we give the answer case by case. Also, the way
        we solve it.

        DERIVATIVES

        We may compute any product, up to 4 factors A,B,C,D or
        any argument up to 4 factors A,B,C,D:

        A*B*C*D             A*B/C/D = A*B/(C*D)
        A*B*C/D             A/B*C/D = A*C/(B*D)
        A*B/C*D             A/B/C*D = A*D/(B*C)
        A/B*C*D =A*C*D/B
        ...                 ...
        A/B/C/D = A/(B*C*D) - we dont need to use brackets to solve any case

        In this version, we may use:

        Integers, Reals (eg. 523.78 or 5.2378E2 ),
        Rational numbers (k/n),
        pi and literal constantes a,b,c,d,e,f,...

        We may use up to 5 nested functions in each factor.

        note: if we need more factors or more nested functions
              it is easy to add.
             
        Below, we can see some of simplified solutions -
        for each function, of course. <<<<<<<< now the result is simplified.
       
note:   log is logarithm of base 10 ;  ten(x) = 10^x ; exp(x)=e^x

functions: exp(x), ten(x), ln(x), log(x), sqr(x),
                  sin(x),cos(x),tan(x),cot(x),sec(x),csc(x),
                  arcsin(x),arccos(x),arctan(x),arccot(x),arcsec(x),arccsc(x),
                  sind(x),cosd(x),tand(x),cotd(x),secd(x),cscd(x),
                  arcsind(x),arccosd(x),arctand(x),arccotd(x),arcsecd(x),arccscd(x), 
                  sinh(x),cosh(x),tanh(x),coth(x),sech(x),csch(x),
                  arcsinh(x),arccosh(x),arctanh(x),arccoth(x),arcsech(x),arccsch(x).

NOTE: if function name ends with d, the argument is in degrees (sind,cosd,...) or
             the result is in degrees (arcsind,arccosd,...)

note: the derivative may be used by the calculator to get the root of a function.


EDIT: It was updated - new version 2017.13, see the last post.  <<<<<<<<<<<<<<<<<<<<<<<
           The file TheCalculator_derivatives25.txt show us  312 examples.

   .
           Thank you all

           Good luck        :t
                       >>>>> ORIGINAL >>> http://masm32.com/board/index.php?topic=175.0

input box=>     [ln((a+b)/(x+pi))   +ln((a+b)/sin(x+pi))]'

solution box1=> -(x+pi)^-1          -cos(x+pi)*sin(x+pi)^-1
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

input box=> [log(x/(3+a))   -log(x/(3+a))   +log(-x/(3+a))  -log(-x/(3+a))
            +log(2*x/(3+a)) -log(2*x/(3+a)) +log(-2*x/(3+a))-log(-2*x/(3+a))
            +log(x^2/(3+a)) -log(x^2/(3+a)) +log(-x^2/(3+a))-log(-x^2/(3+a))
            +log(3*x^2/(3+a))-log(3*x^2/(3+a))+log(-3*x^2/(3+a))-log(-3*x^2/(3+a))
            +log(x^2)       -log(x^2)       +log(-x^2)      -log(-x^2)
            +log(3*x^2)     -log(3*x^2)     +log(-3*x^2)    -log(-3*x^2)
            +log(x^3)       -log(x^3)       +log(-x^3)      -log(-x^3)
            +log(2*x^3)     -log(2*x^3)     +log(-2*x^3)    -log(-2*x^3)
            +log(x/5)       -log(x/5)       +log(-x/5)      -log(-x/5)
            +log(2*x/5)     -log(2*x/5)     +log(-2*x/5)    -log(-2*x/5)
            +log(x^2/5)     -log(x^2/5)     +log(-x^2/5)    -log(-x^2/5)
            +log(3*x^2/5)   -log(3*x^2/5)   +log(-3*x^2/5)  -log(-3*x^2/5)
            +log(x^3/5)     -log(x^3/5)     +log(-x^3/5)    -log(-x^3/5)
            +log(2*x^3/5)   -log(2*x^3/5)   +log(-2*x^3/5)  -log(-2*x^3/5)]'

solution box1=> 1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +6/(ln(10)*x)    -6/(ln(10)*x)   +6/(ln(10)*x)   -6/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)
               +6/(ln(10)*x)    -6/(ln(10)*x)   +6/(ln(10)*x)   -6/(ln(10)*x)
               +1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [log(x/b)       -log(x/b)       +log(-x/b)      -log(-x/b)
            +log(2*x/b)     -log(2*x/b)     +log(-2*x/b)    -log(-2*x/b)
            +log(x^2/b)     -log(x^2/b)     +log(-x^2/b)    -log(-x^2/b)
            +log(3*x^2/b)   -log(3*x^2/b)   +log(-3*x^2/b)  -log(-3*x^2/b)
            +log(x^3/b)     -log(x^3/b)     +log(-x^3/b)    -log(-x^3/b)
            +log(2*x^3/b)   -log(2*x^3/b)   +log(-2*x^3/b)  -log(-2*x^3/b)
            +log(a*x/b)     -log(a*x/b)     +log(-a*x/b)    -log(-a*x/b)
            +log(a*x^2/b)   -log(a*x^2/b)   +log(-a*x^2/b)  -log(-a*x^2/b)
            +log(a*x^3/b)   -log(a*x^3/b)   +log(-a*x^3/b)  -log(-a*x^3/b)]'

solution box1=> 1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)
               +1/(ln(10)*x)    -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)
               +2/(ln(10)*x)    -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)
               +3/(ln(10)*x)    -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)

[RuiLoureiro]

Hi

The Calculator was updated to Calcula71 version 2017.02

Now it simplifies more functions.

Good Luck

++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:04:23

input box=>     [ln(x^-1/b) -ln(x^-1/b) +ln(-x^-1/b)    -ln(-x^-1/b)
                +ln(x^-2/b) -ln(x^-2/b) +ln(-x^-2/b)    -ln(-x^-2/b)
                +ln(x^-3/b) -ln(x^-3/b) +ln(-x^-3/b)    -ln(-x^-3/b)]'

solution box1=> -x^-1       +x^-1      -x^-1           +x^-1
                -2*x^-1     +2*x^-1     -2*x^-1         +2*x^-1
                -3*x^-1     +3*x^-1     -3*x^-1         +3*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:04:40

input box=>     [log(x^-1/b)    -log(x^-1/b)    +log(-x^-1/b)   -log(-x^-1/b)
                +log(x^-2/b)    -log(x^-2/b)    +log(-x^-2/b)   -log(-x^-2/b)
                +log(x^-3/b)    -log(x^-3/b)    +log(-x^-3/b)   -log(-x^-3/b)]'

solution box1=> -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)   +1/(ln(10)*x)
                -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)   +2/(ln(10)*x)
                -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)   +3/(ln(10)*x)

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:05:08

input box=>     [log(x^-1)      -log(x^-1)      +log(-x^-1)     -log(-x^-1)
                +log(x^-2)      -log(x^-2)      +log(-x^-2)     -log(-x^-2)
                +log(x^-3)      -log(x^-3)      +log(-x^-3)     -log(-x^-3)]'

solution box1=> -1/(ln(10)*x)   +1/(ln(10)*x)   -1/(ln(10)*x)   +1/(ln(10)*x)
                -2/(ln(10)*x)   +2/(ln(10)*x)   -2/(ln(10)*x)   +2/(ln(10)*x)
                -3/(ln(10)*x)   +3/(ln(10)*x)   -3/(ln(10)*x)   +3/(ln(10)*x)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:05:24

input box=>     [ln(x^-1)   -ln(x^-1)   +ln(-x^-1)  -ln(-x^-1)
                +ln(x^-2)   -ln(x^-2)   +ln(-x^-2)  -ln(-x^-2)
                +ln(x^-3)   -ln(x^-3)   +ln(-x^-3)  -ln(-x^-3)]'

solution box1=> -x^-1       +x^-1       -x^-1       +x^-1
                -2*x^-1     +2*x^-1     -2*x^-1     +2*x^-1
                -3*x^-1     +3*x^-1     -3*x^-1     +3*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:08:10

input box=>     [ln((x-1)/(x+1))                    -ln((x-1)/(x+1))   
                +ln(-(x-1)/(x+1))                   -ln(-(x-1)/(x+1))]'

solution box1=> (x+1-(x-1))/(x+1)^2*((x+1)/(x-1))   -(x+1-(x-1))/(x+1)^2*((x+1)/(x-1))
                -(-(x+1)+x-1)/(x+1)^2*((x+1)/(x-1)) +(-(x+1)+x-1)/(x+1)^2*((x+1)/(x-1))

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 30-04-2017  23:08:48

input box=>     [log((x-1)/(x+1))                           -log((x-1)/(x+1))
                +log(-(x-1)/(x+1))                          -log(-(x-1)/(x+1))]'

solution box1=> (x+1-(x-1))/(x+1)^2/(ln(10)*(x-1)/(x+1))    -(x+1-(x-1))/(x+1)^2/(ln(10)*(x-1)/(x+1))
                -(-(x+1)+x-1)/(x+1)^2/(ln(10)*(x-1)/(x+1))  +(-(x+1)+x-1)/(x+1)^2/(ln(10)*(x-1)/(x+1))
                THESE ARE NOT SIMPLIFIED... YET.

[RuiLoureiro]

Hi
        The Calculator simplifies more functions.
        I will update it as soon as possible

        Good luck

input box=>     [ln((x-1)/(x+1))    -ln((x-1)/(x+1))    +ln(-(x-1)/(x+1))  -ln(-(x-1)/(x+1))
                +ln((x+1)/(x-1))    -ln((x+1)/(x-1))    +ln(-(x+1)/(x-1))   -ln(-(x+1)/(x-1))
                +ln((1+x)/(1-x))    -ln((1+x)/(1-x))    +ln(-(1+x)/(1-x))   -ln(-(1+x)/(1-x))
               
                +ln((x-a)/(x+b))    -ln((x-a)/(x+b))    +ln(-(x-a)/(x+b))   -ln(-(x-a)/(x+b))
                +ln((x+a)/(x-b))    -ln((x+a)/(x-b))    +ln(-(x+a)/(x-b))   -ln(-(x+a)/(x-b))
                +ln((a+x)/(b-x))    -ln((a+x)/(b-x))    +ln(-(a+x)/(b-x))   -ln(-(a+x)/(b-x))]'

solution box1=> 2/((x+1)*(x-1))     -2/((x+1)*(x-1))    +2/((x+1)*(x-1))    -2/((x+1)*(x-1))
               -2/((x-1)*(x+1))     +2/((x-1)*(x+1))    -2/((x-1)*(x+1))    +2/((x-1)*(x+1))
               +2/((1-x)*(1+x))     -2/((1-x)*(1+x))    +2/((1-x)*(1+x))    -2/((1-x)*(1+x))
               
               +(b+a)/((x+b)*(x-a)) +(-b-a)/((x+b)*(x-a))+(b+a)/((x+b)*(x-a))+(-b-a)/((x+b)*(x-a))
               +(-b-a)/((x-b)*(x+a))+(b+a)/((x-b)*(x+a))+(-b-a)/((x-b)*(x+a))+(b+a)/((x-b)*(x+a))
               +(b+a)/((b-x)*(a+x)) +(-b-a)/((b-x)*(a+x))+(b+a)/((b-x)*(a+x))+(-b-a)/((b-x)*(a+x))

[RuiLoureiro]

Hi all
        TheCalculator was updated.
        This version 2017.03 simplifies more functions
        The file of examples was updated also.
        (see the examples below)

        Good luck  :t
:icon14: 
HERE it is:

input box=>     [ln((x-1)/(x+1))    -ln((x-1)/(x+1))    +ln(-(x-1)/(x+1))   -ln(-(x-1)/(x+1))
                +ln((x+1)/(x-1))    -ln((x+1)/(x-1))    +ln(-(x+1)/(x-1))   -ln(-(x+1)/(x-1))
                +ln((1+x)/(1-x))    -ln((1+x)/(1-x))    +ln(-(1+x)/(1-x))   -ln(-(1+x)/(1-x))
                +ln((x-a)/(x+a))    -ln((x-a)/(x+a))    +ln(-(x-a)/(x+a))   -ln(-(x-a)/(x+a))
                +ln((x+a)/(x-a))    -ln((x+a)/(x-a))    +ln(-(x+a)/(x-a))   -ln(-(x+a)/(x-a))
                +ln((a+x)/(a-x))    -ln((a+x)/(a-x))    +ln(-(a+x)/(a-x))   -ln(-(a+x)/(a-x))
                +ln((x-a)/(x+b))    -ln((x-a)/(x+b))    +ln(-(x-a)/(x+b))   -ln(-(x-a)/(x+b))
                +ln((x+a)/(x-b))    -ln((x+a)/(x-b))    +ln(-(x+a)/(x-b))   -ln(-(x+a)/(x-b))
                +ln((a+x)/(b-x))    -ln((a+x)/(b-x))    +ln(-(a+x)/(b-x))   -ln(-(a+x)/(b-x))]'

solution box1=> 2/((x+1)*(x-1))     -2/((x+1)*(x-1))    +2/((x+1)*(x-1))    -2/((x+1)*(x-1))
               -2/((x-1)*(x+1))     +2/((x-1)*(x+1))    -2/((x-1)*(x+1))    +2/((x-1)*(x+1))
               +2/((1-x)*(1+x))     -2/((1-x)*(1+x))    +2/((1-x)*(1+x))    -2/((1-x)*(1+x))
               +2*a/((x+a)*(x-a))   -2*a/((x+a)*(x-a))  +2*a/((x+a)*(x-a))  -2*a/((x+a)*(x-a))
               -2*a/((x-a)*(x+a))   +2*a/((x-a)*(x+a))  -2*a/((x-a)*(x+a))  +2*a/((x-a)*(x+a))
               +2*a/((a-x)*(a+x))   -2*a/((a-x)*(a+x))  +2*a/((a-x)*(a+x))  -2*a/((a-x)*(a+x))
               +(b+a)/((x+b)*(x-a)) -(b+a)/((x+b)*(x-a))+(b+a)/((x+b)*(x-a))-(b+a)/((x+b)*(x-a))
               -(b+a)/((x-b)*(x+a)) +(b+a)/((x-b)*(x+a))-(b+a)/((x-b)*(x+a))+(b+a)/((x-b)*(x+a))
               +(b+a)/((b-x)*(a+x)) -(b+a)/((b-x)*(a+x))+(b+a)/((b-x)*(a+x))-(b+a)/((b-x)*(a+x))

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [log((x-1)/(x+1))   -log((x-1)/(x+1))   +log(-(x-1)/(x+1))  -log(-(x-1)/(x+1))
                +log((x+1)/(x-1))   -log((x+1)/(x-1))   +log(-(x+1)/(x-1))  -log(-(x+1)/(x-1))
                +log((1+x)/(1-x))   -log((1+x)/(1-x))   +log(-(1+x)/(1-x))  -log(-(1+x)/(1-x))
                +log((x-a)/(x+a))   -log((x-a)/(x+a))   +log(-(x-a)/(x+a))  -log(-(x-a)/(x+a))
                +log((x+a)/(x-a))   -log((x+a)/(x-a))   +log(-(x+a)/(x-a))  -log(-(x+a)/(x-a))
                +log((a+x)/(a-x))   -log((a+x)/(a-x))   +log(-(a+x)/(a-x))  -log(-(a+x)/(a-x))
                +log((x-a)/(x+b))   -log((x-a)/(x+b))   +log(-(x-a)/(x+b))  -log(-(x-a)/(x+b))
                +log((x+a)/(x-b))   -log((x+a)/(x-b))   +log(-(x+a)/(x-b))  -log(-(x+a)/(x-b))
                +log((a+x)/(b-x))   -log((a+x)/(b-x))   +log(-(a+x)/(b-x))  -log(-(a+x)/(b-x))]'

solution box1=> 2/(ln(10)*(x+1)*(x-1))  -2/(ln(10)*(x+1)*(x-1)) +2/(ln(10)*(x+1)*(x-1)) -2/(ln(10)*(x+1)*(x-1))
               -2/(ln(10)*(x-1)*(x+1))  +2/(ln(10)*(x-1)*(x+1)) -2/(ln(10)*(x-1)*(x+1)) +2/(ln(10)*(x-1)*(x+1))
               +2/(ln(10)*(1-x)*(1+x))  -2/(ln(10)*(1-x)*(1+x)) +2/(ln(10)*(1-x)*(1+x)) -2/(ln(10)*(1-x)*(1+x))
               
               +2*a/(ln(10)*(x+a)*(x-a))-2*a/(ln(10)*(x+a)*(x-a))+2*a/(ln(10)*(x+a)*(x-a))-2*a/(ln(10)*(x+a)*(x-a))
               -2*a/(ln(10)*(x-a)*(x+a))+2*a/(ln(10)*(x-a)*(x+a))-2*a/(ln(10)*(x-a)*(x+a))+2*a/(ln(10)*(x-a)*(x+a))
               +2*a/(ln(10)*(a-x)*(a+x))-2*a/(ln(10)*(a-x)*(a+x))+2*a/(ln(10)*(a-x)*(a+x))-2*a/(ln(10)*(a-x)*(a+x))
               
               +(b+a)/(ln(10)*(x+b)*(x-a))-(b+a)/(ln(10)*(x+b)*(x-a))+(b+a)/(ln(10)*(x+b)*(x-a))-(b+a)/(ln(10)*(x+b)*(x-a))
               -(b+a)/(ln(10)*(x-b)*(x+a))+(b+a)/(ln(10)*(x-b)*(x+a))-(b+a)/(ln(10)*(x-b)*(x+a))+(b+a)/(ln(10)*(x-b)*(x+a))
               +(b+a)/(ln(10)*(b-x)*(a+x))-(b+a)/(ln(10)*(b-x)*(a+x))+(b+a)/(ln(10)*(b-x)*(a+x))-(b+a)/(ln(10)*(b-x)*(a+x))

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [ln((x-1)/(x+b))    -ln((x-1)/(x+b))    +ln(-(x-1)/(x+b))   -ln(-(x-1)/(x+b))
                +ln((x+1)/(x-b))    -ln((x+1)/(x-b))    +ln(-(x+1)/(x-b))   -ln(-(x+1)/(x-b))
                +ln((1+x)/(b-x))    -ln((1+x)/(b-x))    +ln(-(1+x)/(b-x))   -ln(-(1+x)/(b-x))]'

solution box1=> (b+1)/((x+b)*(x-1)) -(b+1)/((x+b)*(x-1))+(b+1)/((x+b)*(x-1))-(b+1)/((x+b)*(x-1))
               -(b+1)/((x-b)*(x+1)) +(b+1)/((x-b)*(x+1))-(b+1)/((x-b)*(x+1))+(b+1)/((x-b)*(x+1))
               +(b+1)/((b-x)*(1+x)) -(b+1)/((b-x)*(1+x))+(b+1)/((b-x)*(1+x))-(b+1)/((b-x)*(1+x))
               
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [log((x-1)/(x+b))   -log((x-1)/(x+b))   +log(-(x-1)/(x+b))  -log(-(x-1)/(x+b))
                +log((x+1)/(x-b))   -log((x+1)/(x-b))   +log(-(x+1)/(x-b))  -log(-(x+1)/(x-b))
                +log((1+x)/(b-x))   -log((1+x)/(b-x))   +log(-(1+x)/(b-x))  -log(-(1+x)/(b-x))]'

solution box1=> (b+1)/(ln(10)*(x+b)*(x-1))-(b+1)/(ln(10)*(x+b)*(x-1))+(b+1)/(ln(10)*(x+b)*(x-1))-(b+1)/(ln(10)*(x+b)*(x-1))
               -(b+1)/(ln(10)*(x-b)*(x+1))+(b+1)/(ln(10)*(x-b)*(x+1))-(b+1)/(ln(10)*(x-b)*(x+1))+(b+1)/(ln(10)*(x-b)*(x+1))
               +(b+1)/(ln(10)*(b-x)*(1+x))-(b+1)/(ln(10)*(b-x)*(1+x))+(b+1)/(ln(10)*(b-x)*(1+x))-(b+1)/(ln(10)*(b-x)*(1+x))
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [ln((x-1)/(x+b)^2)  -ln((x-1)/(x+b)^2)  +ln(-(x-1)/(x+b)^2) -ln(-(x-1)/(x+b)^2)
                +ln((x+1)/(x-b)^2)  -ln((x+1)/(x-b)^2)  +ln(-(x+1)/(x-b)^2) -ln(-(x+1)/(x-b)^2)
                +ln((1+x)/(b-x)^2)  -ln((1+x)/(b-x)^2)  +ln(-(1+x)/(b-x)^2) -ln(-(1+x)/(b-x))^2]'

solution box1=>  ( (x+b)^2-2*(x+b)*(x-1))/((x+b)^2*(x-1))
                -( (x+b)^2-2*(x+b)*(x-1))/((x+b)^2*(x-1))
                -(-(x+b)^2+2*(x+b)*(x-1))/((x+b)^2*(x-1))
                +(-(x+b)^2+2*(x+b)*(x-1))/((x+b)^2*(x-1))
                +( (x-b)^2-2*(x-b)*(x+1))/((x-b)^2*(x+1))
                -( (x-b)^2-2*(x-b)*(x+1))/((x-b)^2*(x+1))
                -(-(x-b)^2+2*(x-b)*(x+1))/((x-b)^2*(x+1))
                +(-(x-b)^2+2*(x-b)*(x+1))/((x-b)^2*(x+1))
                +( (b-x)^2+2*(b-x)*(1+x))/((b-x)^2*(1+x))
                -( (b-x)^2+2*(b-x)*(1+x))/((b-x)^2*(1+x))
                +( (b-x)^2+2*(b-x)*(1+x))/((b-x)^2*(1+x))
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [log((x-1)/(x+b)^2) -log((x-1)/(x+b)^2) +log(-(x-1)/(x+b)^2)    -log(-(x-1)/(x+b)^2)
                +log((x+1)/(x-b)^2) -log((x+1)/(x-b)^2) +log(-(x+1)/(x-b)^2)    -log(-(x+1)/(x-b)^2)
                +log((1+x)/(b-x)^2) -log((1+x)/(b-x)^2) +log(-(1+x)/(b-x)^2)    -log(-(1+x)/(b-x))^2]'

solution box1=>  ( (x+b)^2-2*(x+b)*(x-1))/(ln(10)*(x+b)^2*(x-1))
                -( (x+b)^2-2*(x+b)*(x-1))/(ln(10)*(x+b)^2*(x-1))
                -(-(x+b)^2+2*(x+b)*(x-1))/(ln(10)*(x+b)^2*(x-1))
                +(-(x+b)^2+2*(x+b)*(x-1))/(ln(10)*(x+b)^2*(x-1))
                +( (x-b)^2-2*(x-b)*(x+1))/(ln(10)*(x-b)^2*(x+1))
                -( (x-b)^2-2*(x-b)*(x+1))/(ln(10)*(x-b)^2*(x+1))
                -(-(x-b)^2+2*(x-b)*(x+1))/(ln(10)*(x-b)^2*(x+1))
                +(-(x-b)^2+2*(x-b)*(x+1))/(ln(10)*(x-b)^2*(x+1))
                +( (b-x)^2+2*(b-x)*(1+x))/(ln(10)*(b-x)^2*(1+x))
                -( (b-x)^2+2*(b-x)*(1+x))/(ln(10)*(b-x)^2*(1+x))
                +( (b-x)^2+2*(b-x)*(1+x))/(ln(10)*(b-x)^2*(1+x))

[RuiLoureiro]

Hi
        This is TheCalculator powerful version 2017.04.
        It was updated today (Calcula73) -see FIRST POST
               
        (see examples about all functions below)

Guga,
          why do i need wolfram... ?
          (For me) TheCalculator does it better
          (it does what i want)

        Good luck
:icon14:

input box=> [a^((x-1)/(x+1))+exp((x-1)/(x+1))+e^((x-1)/(x+1))+10^((x-1)/(x+1))+ten((x-1)/(x+1))+ln((x-1)/(x+1))+lo
g((x-1)/(x+1))+sqr((x-1)/(x+1))+sin((x-1)/(x+1))+cos((x-1)/(x+1))+tan((x-1)/(x+1))+cot((x-1)/(x+1))+sec((x-1)/(x+1
))+csc((x-1)/(x+1))+arcsin((x-1)/(x+1))+arccos((x-1)/(x+1))+arctan((x-1)/(x+1))+arccot((x-1)/(x+1))+arcsec((x-1)/(
x+1))+arccsc((x-1)/(x+1))+sind((x-1)/(x+1))+cosd((x-1)/(x+1))+tand((x-1)/(x+1))+cotd((x-1)/(x+1))+secd((x-1)/(x+1)
)+cscd((x-1)/(x+1))+arcsind((x-1)/(x+1))+arccosd((x-1)/(x+1))+arctand((x-1)/(x+1))+arccotd((x-1)/(x+1))+arcsecd((x
-a)/(x+1))+arccscd((x-1)/(x+1))+sinh((x-1)/(x+1))+cosh((x-1)/(x+1))+tanh((x-1)/(x+1))+coth((x-1)/(x+1))+sech((x-1)
/(x+1))+csch((x-1)/(x+1))+arcsinh((x-1)/(x+1))+arccosh((x-1)/(x+1))+arctanh((x-1)/(x+1))+arccoth((x-1)/(x+1))+arcs
ech((x-1)/(x+1))+arccsch((x-1)/(x+1))]'

solution box1=> ln(a)*2/(x+1)^2*a^((x-1)/(x+1))+2/(x+1)^2*exp((x-1)/(x+1))+2/(x+1)^2*e^((x-1)/(x+1))+ln(10)*2/(x+1)^2*10^((x-1)/(x+1))+2/(x+1)^2*ln(10)*ten(x)+2/((x+1)*(x-1))+2/(ln(10)*x*(x-1))+2/(x+1)^2/(2*sqr((x-1)/(x+1)))+2/(
x+1)^2*cos((x-1)/(x+1))-2/(x+1)^2*sin((x-1)/(x+1))+2/(x+1)^2*sec((x-1)/(x+1))^2-2/(x+1)^2*csc((x-1)/(x+1))^2+2/(x+
1)^2*sec((x-1)/(x+1))*tan((x-1)/(x+1))-2/(x+1)^2*csc((x-1)/(x+1))*cot((x-1)/(x+1))+2/(x+1)^2/sqr(1-((x-1)/(x+1))^2
)-2/(x+1)^2/sqr(1-((x-1)/(x+1))^2)+2/(x+1)^2/(1+((x-1)/(x+1))^2)-2/(x+1)^2/(1+((x-1)/(x+1))^2)+2/(x+1)^2/(abs((x-1
)/(x+1))*sqr(((x-1)/(x+1))^2-1))-2/(x+1)^2/(abs((x-1)/(x+1))*sqr(((x-1)/(x+1))^2-1))+2/(x+1)^2*cosd((x-1)/(x+1))-2
/(x+1)^2*sind((x-1)/(x+1))+2/(x+1)^2*secd((x-1)/(x+1))^2-2/(x+1)^2*cscd((x-1)/(x+1))^2+2/(x+1)^2*secd((x-1)/(x+1))
*tand((x-1)/(x+1))-2/(x+1)^2*cscd((x-1)/(x+1))*cotd((x-1)/(x+1))+2/(x+1)^2/sqr(1-((x-1)/(x+1))^2)-2/(x+1)^2/sqr(1-
((x-1)/(x+1))^2)+2/(x+1)^2/(1+((x-1)/(x+1))^2)-2/(x+1)^2/(1+((x-1)/(x+1))^2)+(1+a)/(x+1)^2/(abs((x-a)/(x+1))*sqr((
(x-a)/(x+1))^2-1))-2/(x+1)^2/(abs((x-1)/(x+1))*sqr(((x-1)/(x+1))^2-1))+2/(x+1)^2*cosh((x-1)/(x+1))+2/(x+1)^2*sinh(
(x-1)/(x+1))+2/(x+1)^2*sech((x-1)/(x+1))^2-2/(x+1)^2*csch((x-1)/(x+1))^2+2/(x+1)^2*sech((x-1)/(x+1))*tanh((x-1)/(x
+1))-2/(x+1)^2*csch((x-1)/(x+1))*coth((x-1)/(x+1))+2/(x+1)^2/sqr(((x-1)/(x+1))^2+1)-2/(x+1)^2/sqr(((x-1)/(x+1))^2-
1)+2/(x+1)^2/(1-((x-1)/(x+1))^2)+2/(x+1)^2/(1-((x-1)/(x+1))^2)-2/(x+1)^2/((x-1)/x*sqr(1-((x-1)/(x+1))^2))-2/(x+1)^
2/(abs((x-1)/(x+1))*sqr(1+((x-1)/(x+1))^2))

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [a^((x-a)*(x-b))+exp((x-a)*(x-b))+e^((x-a)*(x-b))+10^((x-a)*(x-b))+ten((x-a)*(x-b))+ln((x-a)*(x-b))+lo
g((x-a)*(x-b))+sqr((x-a)*(x-b))+sin((x-a)*(x-b))+cos((x-a)*(x-b))+tan((x-a)*(x-b))+cot((x-a)*(x-b))+sec((x-a)*(x-b
))+csc((x-a)*(x-b))+arcsin((x-a)*(x-b))+arccos((x-a)*(x-b))+arctan((x-a)*(x-b))+arccot((x-a)*(x-b))+arcsec((x-a)*(
x-b))+arccsc((x-a)*(x-b))+sind((x-a)*(x-b))+cosd((x-a)*(x-b))+tand((x-a)*(x-b))+cotd((x-a)*(x-b))+secd((x-a)*(x-b)
)+cscd((x-a)*(x-b))+arcsind((x-a)*(x-b))+arccosd((x-a)*(x-b))+arctand((x-a)*(x-b))+arccotd((x-a)*(x-b))+arcsecd((x
-a)*(x-b))+arccscd((x-a)*(x-b))+sinh((x-a)*(x-b))+cosh((x-a)*(x-b))+tanh((x-a)*(x-b))+coth((x-a)*(x-b))+sech((x-a)
*(x-b))+csch((x-a)*(x-b))+arcsinh((x-a)*(x-b))+arccosh((x-a)*(x-b))+arctanh((x-a)*(x-b))+arccoth((x-a)*(x-b))+arcs
ech((x-a)*(x-b))+arccsch((x-a)*(x-b))+a^((1-x)*(1+x))+exp((1-x)*(1+x))+e^((1-x)*(1+x))+10^((1-x)*(1+x))+ten((1-x)*
(1+x))+ln((1-x)*(1+x))+log((1-x)*(1+x))+sqr((1-x)*(1+x))+sin((1-x)*(1+x))+cos((1-x)*(1+x))+tan((1-x)*(1+x))+cot((1
-x)*(1+x))+sec((1-x)*(1+x))+csc((1-x)*(1+x))+arcsin((1-x)*(1+x))+arccos((1-x)*(1+x))+arctan((1-x)*(1+x))+arccot((1
-x)*(1+x))+arcsec((1-x)*(1+x))+arccsc((1-x)*(1+x))+sind((1-x)*(1+x))+cosd((1-x)*(1+x))+tand((1-x)*(1+x))+cotd((1-x
)*(1+x))+secd((1-x)*(1+x))+cscd((1-x)*(1+x))+arcsind((1-x)*(1+x))+arccosd((1-x)*(1+x))+arctand((1-x)*(1+x))+arccot
d((1-x)*(1+x))+arcsecd((x-a)*(1+x))+arccscd((1-x)*(1+x))+sinh((1-x)*(1+x))+cosh((1-x)*(1+x))+tanh((1-x)*(1+x))+cot
h((1-x)*(1+x))+sech((1-x)*(1+x))+csch((1-x)*(1+x))+arcsinh((1-x)*(1+x))+arccosh((1-x)*(1+x))+arctanh((1-x)*(1+x))+
arccoth((1-x)*(1+x))+arcsech((1-x)*(1+x))+arccsch((1-x)*(1+x))]'

solution box1=> ln(a)*(-b-a+2*x)*a^((x-a)*(x-b))+(-b-a+2*x)*exp((x-a)*(x-b))+(-b-a+2*x)*e^((x-a)*(x-b))+ln(10)*(-b
-a+2*x)*10^((x-a)*(x-b))+(-b-a+2*x)*ln(10)*ten(x)+(-b-a+2*x)/((x-a)*(x-b))+(-b-a+2*x)/(ln(10)*(x-a)*(x-b))+(-b-a+2
*x)/(2*sqr((x-a)*(x-b)))+(-b-a+2*x)*cos((x-a)*(x-b))+(b+a-2*x)*sin((x-a)*(x-b))+(-b-a+2*x)*sec((x-a)*(x-b))^2+(b+a
-2*x)*csc((x-a)*(x-b))^2+(-b-a+2*x)*sec((x-a)*(x-b))*tan((x-a)*(x-b))+(b+a-2*x)*csc((x-a)*(x-b))*cot((x-a)*(x-b))+
(-b-a+2*x)/sqr(1-((x-a)*(x-b))^2)+(b+a-2*x)/sqr(1-((x-a)*(x-b))^2)+(-b-a+2*x)/(1+((x-a)*(x-b))^2)+(b+a-2*x)/(1+((x
-a)*(x-b))^2)+(-b-a+2*x)/(abs((x-a)*(x-b))*sqr(((x-a)*(x-b))^2-1))+(b+a-2*x)/(abs((x-a)*(x-b))*sqr(((x-a)*(x-b))^2
-1))+(-b-a+2*x)*cosd((x-a)*(x-b))+(b+a-2*x)*sind((x-a)*(x-b))+(-b-a+2*x)*secd((x-a)*(x-b))^2+(b+a-2*x)*cscd((x-a)*
(x-b))^2+(-b-a+2*x)*secd((x-a)*(x-b))*tand((x-a)*(x-b))+(b+a-2*x)*cscd((x-a)*(x-b))*cotd((x-a)*(x-b))+(-b-a+2*x)/s
qr(1-((x-a)*(x-b))^2)+(b+a-2*x)/sqr(1-((x-a)*(x-b))^2)+(-b-a+2*x)/(1+((x-a)*(x-b))^2)+(b+a-2*x)/(1+((x-a)*(x-b))^2
)+(-b-a+2*x)/(abs((x-a)*(x-b))*sqr(((x-a)*(x-b))^2-1))+(b+a-2*x)/(abs((x-a)*(x-b))*sqr(((x-a)*(x-b))^2-1))+(-b-a+2
*x)*cosh((x-a)*(x-b))+(-b-a+2*x)*sinh((x-a)*(x-b))+(-b-a+2*x)*sech((x-a)*(x-b))^2+(b+a-2*x)*csch((x-a)*(x-b))^2+(-
b-a+2*x)*sech((x-a)*(x-b))*tanh((x-a)*(x-b))+(b+a-2*x)*csch((x-a)*(x-b))*coth((x-a)*(x-b))+(-b-a+2*x)/sqr(((x-a)*(
x-b))^2+1)+(b+a-2*x)/sqr(((x-a)*(x-b))^2-1)+(-b-a+2*x)/(1-((x-a)*(x-b))^2)+(-b-a+2*x)/(1-((x-a)*(x-b))^2)+(b+a-2*x
)/((x-a)*(x-b)*sqr(1-((x-a)*(x-b))^2))+(b+a-2*x)/(abs((x-a)*(x-b))*sqr(1+((x-a)*(x-b))^2))+ln(a)-2*x*a^((1-x)*(1+x
))-2*x*exp((1-x)*(1+x))-2*x*e^((1-x)*(1+x))+ln(10)-2*x*10^((1-x)*(1+x))-2*x*ln(10)*ten(x)-2*x/((1-x)*(1+x))-2*x/(l
n(10)*(1-x)*(1+x))+2*x/(2*sqr((1-x)*(1+x)))-2*x*cos((1-x)*(1+x))-2*x*sin((1-x)*(1+x))-2*x*sec((1-x)*(1+x))^2-2*x*c
sc((1-x)*(1+x))^2-2*x*sec((1-x)*(1+x))*tan((1-x)*(1+x))-2*x*csc((1-x)*(1+x))*cot((1-x)*(1+x))+2*x/sqr(1-((1-x)*(1+
x))^2)-2*x/sqr(1-((1-x)*(1+x))^2)+2*x/(1+((1-x)*(1+x))^2)-2*x/(1+((1-x)*(1+x))^2)+2*x/(abs((1-x)*(1+x))*sqr(((1-x)
*(1+x))^2-1))-2*x/(abs((1-x)*(1+x))*sqr(((1-x)*(1+x))^2-1))-2*x*cosd((1-x)*(1+x))-2*x*sind((1-x)*(1+x))-2*x*secd((
1-x)*(1+x))^2-2*x*cscd((1-x)*(1+x))^2-2*x*secd((1-x)*(1+x))*tand((1-x)*(1+x))-2*x*cscd((1-x)*(1+x))*cotd((1-x)*(1+
x))+2*x/sqr(1-((1-x)*(1+x))^2)-2*x/sqr(1-((1-x)*(1+x))^2)+2*x/(1+((1-x)*(1+x))^2)-2*x/(1+((1-x)*(1+x))^2)+(1-a+2*x
)/(abs((x-a)*(1+x))*sqr(((x-a)*(1+x))^2-1))-2*x/(abs((1-x)*(1+x))*sqr(((1-x)*(1+x))^2-1))-2*x*cosh((1-x)*(1+x))-2*
x*sinh((1-x)*(1+x))-2*x*sech((1-x)*(1+x))^2-2*x*csch((1-x)*(1+x))^2-2*x*sech((1-x)*(1+x))*tanh((1-x)*(1+x))-2*x*cs
ch((1-x)*(1+x))*coth((1-x)*(1+x))+2*x/sqr(((1-x)*(1+x))^2+1)-2*x/sqr(((1-x)*(1+x))^2-1)+2*x/(1-((1-x)*(1+x))^2)+2*
x/(1-((1-x)*(1+x))^2)-2*x/((1-x)*x*sqr(1-((1-x)*(1+x))^2))-2*x/(abs((1-x)*(1+x))*sqr(1+((1-x)*(1+x))^2))

[HSE]

Hi Rui!!

So far what i tested is perfect :t

[RuiLoureiro]

Hi Rui!!

So far what i tested is perfect :t

Hi HSE,
            Gracias, obrigado, thank you for all.  :t
            Try 10^((x-1)/(x+1)) in wolframalpha and TheCalculator version 2017.04
            We get something like ... (to me rubbish).
            They corrected a^(same thing above).
            Try also a^(x+1)/(x+1) -- ( with a or 10).
            Wait for the next version 2017.05 to get derivatives of
            arguments (a*x+b)/(c*x+d). Next version will do
             expressions up to 9000 characters. So we may test
             large expressions [A+B+C+D+E+...]'
EDIT:  the next version has a structure of 584 428 bytes divided up into 3 areas:
           normal, reserved and auxiliary or extra, each one divided in 6 groups:A,B,C,D,E,F...
              Previous versions have a problem with function ten(x): doesnt work correctly.

[RuiLoureiro]

Hi,
        Here it is TheCalculator version 2017.05
        A great number of solutions are simplified.
        Now, it uses a new structure to solve any function.

        Good luck
       
note1:  Any solution given by TheCalculator has not syntax errors
        if it doesnt show any syntax error.
       
note2:  In the file TheCalculator_derivatives12.txt
        we may find 101 examples using almost all functions
        with many different arguments.

input box=>     [(x-1)*(x+1)+(x-1)/(x+1)+(x-1)*(x+3)+(x-1)/(x+3)]'
   
solution box1=> 2   +4*x    +2/(x+1)^2  +4/(x+3)^2          <<<<--- very simple

++ 84 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [(x-1)*(x+1)*(x+3)]'

solution box1=> x*(x+3)+x*(x+3)+x^2                          <<<<--- need more simplification yet

++ 85 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [a^((2*x-1)/(3*x+5))        +exp((2*x-1)/(3*x+5))       
            +e^((2*x-1)/(3*x+5))        +10^((2*x-1)/(3*x+5))
            +ten((2*x-1)/(3*x+5))       +ln((2*x-1)/(3*x+5))       
            +log((2*x-1)/(3*x+5))       +sqr((2*x-1)/(3*x+5))

            +sin((2*x-1)/(3*x+5))       +cos((2*x-1)/(3*x+5))       
            +tan((2*x+1)/(3*x+5))       +cot((2*x-1)/(3*x+5))
            +sec((2*x-1)/(3*x+5))       +csc((2*x-1)/(3*x+5))       
            +arcsin((2*x-1)/(3*x+5))    +arccos((2*x-1)/(3*x+5))
            +arctan((2*x-1)/(3*x+5))    +arccot((2*x-1)/(3*x+5))   
            +arcsec((2*x-1)/(3*x+5))    +arccsc((2*x-1)/(3*x+5))

            +sind((2*x+1)/(3*x+5))      +cosd((2*x-1)/(3*x+5))     
            +tand((2*x-1)/(3*x+5))      +cotd((2*x-1)/(3*x+5))
            +secd((2*x-1)/(3*x+5))      +cscd((2*x-1)/(3*x+5))     
            +arcsind((2*x-1)/(3*x+5))   +arccosd((2*x-1)/(3*x+5))
            +arctand((2*x-1)/(3*x+5))   +arccotd((2*x-1)/(3*x+5))   
            +arcsecd((2*x-1)/(3*x+5))   +arccscd((2*x-1)/(3*x+5))

            +sinh((2*x-1)/(3*x+5))      +cosh((2*x-1)/(3*x+5))     
            +tanh((2*x-1)/(3*x+5))      +coth((2*x-1)/(3*x+5))
            +sech((2*x-1)/(3*x+5))      +csch((2*x-1)/(3*x+5))     
            +arcsinh((2*x-1)/(3*x+5))   +arccosh((2*x-1)/(3*x+5))
            +arctanh((2*x-1)/(3*x+5))   +arccoth((2*x-1)/(3*x+5))   
            +arcsech((2*x-1)/(3*x+5))   +arccsch((2*x-1)/(3*x+5))]'

solution box1=>
           ln(a)*(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*a^((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*exp((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*e^((2*x-1)/(3*x+5))
         +ln(10)*(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*10^((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*ln(10)*ten((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/((3*x+5)*(2*x-1))
                +(2*(3*x+5)-3*(2*x-1))/(ln(10)*(3*x+5)*(2*x-1))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(2*sqr((2*x-1)/(3*x+5)))
               
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*cos((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sin((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x+1))/(3*x+5)^2*sec((2*x+1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*csc((2*x-1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sec((2*x-1)/(3*x+5))*tan((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*csc((2*x-1)/(3*x+5))*cot((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1+((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1+((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(abs((2*x-1)/(3*x+5))*sqr(((2*x-1)/(3*x+5))^2-1))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(abs((2*x-1)/(3*x+5))*sqr(((2*x-1)/(3*x+5))^2-1))
                +(2*(3*x+5)-3*(2*x+1))/(3*x+5)^2*cosd((2*x+1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sind((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*secd((2*x-1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*cscd((2*x-1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*secd((2*x-1)/(3*x+5))*tand((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*cscd((2*x-1)/(3*x+5))*cotd((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1+((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1+((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(abs((2*x-1)/(3*x+5))*sqr(((2*x-1)/(3*x+5))^2-1))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(abs((2*x-1)/(3*x+5))*sqr(((2*x-1)/(3*x+5))^2-1))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*cosh((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sinh((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sech((2*x-1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*csch((2*x-1)/(3*x+5))^2
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*sech((2*x-1)/(3*x+5))*tanh((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2*csch((2*x-1)/(3*x+5))*coth((2*x-1)/(3*x+5))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(((2*x-1)/(3*x+5))^2+1)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/sqr(((2*x-1)/(3*x+5))^2-1)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(1-((2*x-1)/(3*x+5))^2)
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/((2*x-1)/(3*x+5)*sqr(1-((2*x-1)/(3*x+5))^2))
                +(2*(3*x+5)-3*(2*x-1))/(3*x+5)^2/(abs((2*x-1)/(3*x+5))*sqr(1+((2*x-1)/(3*x+5))^2))

+++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(x+cos((a*x+b)/(c*x+d)))]'

solution box1=> (1+(a*(c*x+d)-c*(a*x+b))/(c*x+d)^2*sin((a*x+b)/(c*x+d)))*cos(x+cos((a*x+b)/(c*x+d)))

+++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(x+cos((a*x+b)^2/(c*x+d)^3))]'

solution box1=> (1+(2*a*(a*x+b)-(a*x+b)^2*3*c*(c*x+d)^2)/(c*x+d)^6*sin((a*x+b)^2/(c*x+d)^3))*cos(x+cos((a*x+b)^2/(
c*x+d)^3))

++ 88 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(2*pi*x+cos((1/2)*pi*x+log((a*x+b)^2/(c*x+d)^3)))]'

solution box1=> (2*pi+(pi*(1/2)+(2*a*(a*x+b)-(a*x+b)^2*3*c*(c*x+d)^2)/(c*x+d)^6/(ln(10)*(a*x+b)^2/(c*x+d)^3))
                *sin((1/2)*pi*x+log((a*x+b)^2/(c*x+d)^3)))*cos(2*pi*x+cos((1/2)*pi*x+log((a*x+b)^2/(c*x+d)^3)))
               
++ 89 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [2*pi*x+cos((1/2)*pi*x+log((a*x+b)^2/(c*x+d)^3))]'

solution box1=> 2*pi+(pi*(1/2)+(2*a*(a*x+b)-(a*x+b)^2*3*c*(c*x+d)^2)/(c*x+d)^6/(ln(10)*(a*x+b)^2/(c*x+d)^3))
                *sin((1/2)*pi*x+log((a*x+b)^2/(c*x+d)^3))

++ 90 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(2*pi*x+a)^(1/2) * cos(pi/2*x+b)^(2/3)]'

solution box1=> (2*pi)/2*cos(2*pi*x+a)*sin(2*pi*x+a)^-(1/2)*cos(pi/2*x+b)^(2/3)
                        -sin(2*pi*x+a)^(1/2)*(2/3)*(pi/2)*sin(pi/2*x+b)*cos(pi/2*x+b)^-(1/3)

++ 91 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [sin(x)^(1/3)*cos(x)^(1/4)*tan(x)^(2/3)*sec(x)^(3/4)]'

solution box1=>       cos(x)/3*sin(x)^-(2/3)*cos(x)^(1/4)*tan(x)^(2/3)*sec(x)^(3/4)
               +(1/4)*sin(x)*cos(x)^-(3/4)*sin(x)^(1/3)*tan(x)^(2/3)*sec(x)^(3/4)
               +(2/3)*sec(x)^2*tan(x)^-(1/3)*sin(x)^(1/3)*cos(x)^(1/4)*sec(x)^(3/4)
               +(3/4)*sec(x)*tan(x)*sec(x)^-(1/4)*sin(x)^(1/3)*cos(x)^(1/4)*tan(x)^(2/3)

++ 92 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [(a*x+b)^(1/3)*(c*x+d)^(2/3)]'

solution box1=> a*(1/3)*(a*x+b)^-(2/3)*(c*x+d)^(2/3)+(a*x+b)^(1/3)*c*(2/3)*(c*x+d)^-(1/3)

++ 93 +++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [(a*x+b)^(1/2)*(c*x+d)^(2/3)/(f*x+g)^(1/3)]'

solution box1=> ((a*(1/2)*(a*x+b)^-(1/2)*(c*x+d)^(2/3)+(a*x+b)^(1/2)*c*(2/3)*(c*x+d)^-(1/3))*(f*x+g)^(1/3)-(a*x+b)
^(1/2)*(c*x+d)^(2/3)*f*(1/3)*(f*x+g)^-(2/3))/(f*x+g)^(2/3)

++ 94 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(1-x^2)/cos((3/2)*pi*x)^(1/3)]'

solution box1=> ( -2*x*cos((3/2)*pi*x)^(1/3)
                  +(1/3)*pi*(3/2)*sin((3/2)*pi*x)*cos((3/2)*pi*x)^-(2/3)*(1-x^2)
                ) / cos((3/2)*pi*x)^(2/3)

++ 95 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x+b)^(1/2)*(c*x+d)^(2/3)/(f*x+g)^(1/2)]'

solution box1=> ((a*(1/2)*(a*x+b)^-(1/2)*(c*x+d)^(2/3)+(a*x+b)^(1/2)*c*(2/3)*(c*x+d)^-(1/3))*(f*x+g)^(1/2)-(a*x+b)
^(1/2)*(c*x+d)^(2/3)*f*(1/2)*(f*x+g)^-(1/2))/(f*x+g)

++ 96 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(1-x^2)/cos((3/2)*pi*x)^(1/2)]'

solution box1=> (-2*x*cos((3/2)*pi*x)^(1/2)+(1/2)*pi*(3/2)*sin((3/2)*pi*x)*cos((3/2)*pi*x)^-(1/2)*(1-x^2))/cos((3/
2)*pi*x)

++ 97 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x+b)^2*(c*x+d)^2/(f*x+g)^(1/2)]'

solution box1=> ((2*a*(a*x+b)*(c*x+d)^2+(a*x+b)^2*2*c*(c*x+d))*(f*x+g)^(1/2)-(a*x+b)^2*(c*x+d)^2*f*(1/2)
*(f*x+g)^-(1/2))/(f*x+g)

++ 98 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [sin(a*x+b)^2*cos(c*x+d)^2/(f*x+g)^(1/2)]'

solution box1=> ((2*a*cos(a*x+b)*sin(a*x+b)*cos(c*x+d)^2-sin(a*x+b)^2*2*c*sin(c*x+d)*cos(c*x+d))*(f*x+g)^(1/2)-sin
(a*x+b)^2*cos(c*x+d)^2*f*(1/2)*(f*x+g)^-(1/2))/(f*x+g)

++ 99 +++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(sin(x+b)^2*cos(x+d)^3/(f*x+g))]'

solution box1=> ((2*cos(x+b)*sin(x+b)*cos(x+d)^3-sin(x+b)^2*3*sin(x+d)*cos(x+d)^2)*(f*x+g)-f*sin(x+b)^2*cos(x+d)^3
)/(f*x+g)^2*(f*x+g)/(sin(x+b)^2*cos(x+d)^3)

++ 100 ++++++++++++++++++++++++++++++++++++++++++++++
input box=> [log(sin(x+b)^2  * cos(x+d)^3  /  (f*x+g))]'

solution box1=> ((2*cos(x+b)*sin(x+b)*cos(x+d)^3-sin(x+b)^2*3*sin(x+d)*cos(x+d)^2)*(f*x+g)-f*sin(x+b)^2*cos(x+d)^3
)/(ln(10)*(f*x+g)*sin(x+b)^2*cos(x+d)^3)

[RuiLoureiro]

Hi,
        Here is the more powerful version 2017.06 of TheCalculator.

        The computational engine used in this version
        uses a structure of 810 524 bytes divided up into
        5 different ares: Normal, Reserved, Auxiliary, Extra
        and Magic. Each one is divided in 6 blocks A,B,C,D,E,F
        of variables. In this way, TheCalculator should solve
        any complex expression without any problem or conflict.

        Good luck
:icon14:         
note1:  The computational engine uses advanced computational
        concepts as well as a great set of well designed macros
        and well designed set of basic procedures to do
        simple things: Mov, Add, Rem, etc. etc.
        All buffers, variables, etc. etc, are aligned by 16.
        Almost all macros have a veriosn YES and a version NOT.
       
note2:  This new version 2017.06 -Calcula75.exe- uses new
        and improved procedures to get function maps,
        bracket maps and power maps- max = 256.
         
note3:  In the file TheCalculator_derivatives13.txt
        we may find 123 examples using almost all functions
        with many different arguments.

HERE 6 examples

input box=> [(x-1)*(x+1)+(x-1)/(x+1)+(x-1)*(x+3)+(x-1)/(x+3)]'

solution box1=> 2+4*x+2/(x+1)^2+4/(x+3)^2                   <<<< very simple

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(x-1)*(x+1)*(x+3)]'

solution box1=> 2*x*(x+3)+x^2                               <<<< simplified

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x+b)^(1/3)*(c*x+d)^(2/3)/(f*x+g)^(1/2)]'

solution box1=> ((a*(1/3)*(a*x+b)^-(2/3)*(c*x+d)^(2/3)+(a*x+b)^(1/3)*c*(2/3)*(c*x+d)^-(1/3))*(f*x+g)^(1/2)-(a*x+b)
^(1/3)*(c*x+d)^(2/3)*f*(1/2)*(f*x+g)^-(1/2))/(f*x+g)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x^2+b*x+c)*(d*x^2+f*x+g)]'

solution box1=> (a*2*x+b)*(d*x^2+f*x+g)+(d*2*x+f)*(a*x^2+b*x+c)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x^2+b*x+c)^2*(d*x^2+f*x+g)^3]'

solution box1=> 2*(a*2*x+b)*(a*x^2+b*x+c)*(d*x^2+f*x+g)^3+(a*x^2+b*x+c)^2*3*(d*2*x+f)*(d*x^2+f*x+g)^2

++ 123 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x^2+b*x+c)^-2/(d*x^2+f*x+g)^3]'

solution box1=> -(2*(a*2*x+b)*(a*x^2+b*x+c)^-3+(a*x^2+b*x+c)^-2*3*(d*2*x+f)*(d*x^2+f*x+g)^2)/(d*x^2+f*x+g)^6

HERE more complex examples

input box=>     [(a*x^2+b*x+c)*(d*x^2+f*x+g)]'

solution box1=> (a*2*x+b)*(d*x^2+f*x+g)+(d*2*x+f)*(a*x^2+b*x+c)

version 2017.07 only:
solution box1=> (2*a*x+b)*(d*x^2+f*x+g)+(2*d*x+f)*(a*x^2+b*x+c)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x^2+b*x+c)^2*(d*x^2+f*x+g)^3]'

solution box1=> 2*(a*2*x+b)*(a*x^2+b*x+c)*(d*x^2+f*x+g)^3+(a*x^2+b*x+c)^2*3*(d*2*x+f)*(d*x^2+f*x+g)^2
++ 123 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(a*x^2+b*x+c)^-2/(d*x^2+f*x+g)^3]'

solution box1=> -(2*(a*2*x+b)*(a*x^2+b*x+c)^-3+(a*x^2+b*x+c)^-2*3*(d*2*x+f)*(d*x^2+f*x+g)^2)/(d*x^2+f*x+g)^6

version 2017.07 only:
solution box1=> -(2*(2*a*x+b)*(a*x^2+b*x+c)^-3+(a*x^2+b*x+c)^-2*3*(2*d*x+f)*(d*x^2+f*x+g)^2)/(d*x^2+f*x+g)^6
++ 124 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 21-05-2017  15:17:08

input box=>     [(2*x-1)^3*(3*x+2)^2/(1/2)*(f*x+g)^(1/2)]'

solution box1=> (  6*(2*x-1)^2*(3*x+2)^2*(f*x+g)^(1/2)
                   +6*(3*x+2)*(2*x-1)^3*(f*x+g)^(1/2)
                   +(1/2)*f*(f*x+g)^-(1/2)*(2*x-1)^3*(3*x+2)^2
                ) / (1/2)
++ 125 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 21-05-2017  15:24:10

input box=>     [sin(x+cos(x-tan(x*cot(x))))   ]'

solution box1=> (1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))
++ 126 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 21-05-2017  15:29:03

input box=> [sin(x+cos(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))]'

solution box1=> (1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))*cos(x
+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))+(1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x)))
)*sin(x+cos(x-tan(x*cot(x))))*sin(x+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))+(1+(1+(cot(x)-x*csc(x)^2)*se
c(x*cot(x))^2)*sin(x-tan(x*cot(x))))*sec(x+cos(x-tan(x*cot(x))))^2*sin(x+cos(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*c
ot(x))))
++ 127 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 21-05-2017  15:31:30

input box=> [sin(x+cos(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))*ten(x+cos(x-tan(x
*cot(x))))]'

solution box1=> (1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))*cos(x
+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))*ten(x+cos(x-tan(x*cot(x))))+(1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot
(x))^2)*sin(x-tan(x*cot(x))))*sin(x+cos(x-tan(x*cot(x))))*sin(x+cos(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))*
ten(x+cos(x-tan(x*cot(x))))+(1+(1+(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x))))*sec(x+cos(x-tan(x*cot
(x))))^2*sin(x+cos(x-tan(x*cot(x))))*cos(x+cos(x-tan(x*cot(x))))*ten(x+cos(x-tan(x*cot(x))))+(1+(1+(cot(x)-x*csc(x
)^2)*sec(x*cot(x))^2)*sin(x-tan(x*cot(x))))*ln(10)*ten(x+cos(x-tan(x*cot(x))))*sin(x+cos(x-tan(x*cot(x))))*cos(x+c
os(x-tan(x*cot(x))))*tan(x+cos(x-tan(x*cot(x))))
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Sunday, 21-05-2017  15:44:57

input box=> [sin(x*cos(x*tan(x*cot(x))))*cos(x*cos(x*tan(x*cot(x))))*tan(x*cos(x*tan(x*cot(x))))*ten(x*cos(x*tan(x
*cot(x))))]'

solution box1=> (cos(x*tan(x*cot(x)))-x*(tan(x*cot(x))+x*(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x*tan(x*cot(x)))
)*cos(x*cos(x*tan(x*cot(x))))*cos(x*cos(x*tan(x*cot(x))))*tan(x*cos(x*tan(x*cot(x))))*ten(x*cos(x*tan(x*cot(x))))+
(cos(x*tan(x*cot(x)))-x*(tan(x*cot(x))+x*(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x*tan(x*cot(x))))*sin(x*cos(x*ta
n(x*cot(x))))*sin(x*cos(x*tan(x*cot(x))))*tan(x*cos(x*tan(x*cot(x))))*ten(x*cos(x*tan(x*cot(x))))+(cos(x*tan(x*cot
(x)))-x*(tan(x*cot(x))+x*(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x*tan(x*cot(x))))*sec(x*cos(x*tan(x*cot(x))))^2*
sin(x*cos(x*tan(x*cot(x))))*cos(x*cos(x*tan(x*cot(x))))*ten(x*cos(x*tan(x*cot(x))))+(cos(x*tan(x*cot(x)))-x*(tan(x
*cot(x))+x*(cot(x)-x*csc(x)^2)*sec(x*cot(x))^2)*sin(x*tan(x*cot(x))))*ln(10)*ten(x*cos(x*tan(x*cot(x))))*sin(x*cos
(x*tan(x*cot(x))))*cos(x*cos(x*tan(x*cot(x))))*tan(x*cos(x*tan(x*cot(x))))

[RuiLoureiro]

Hi all,
        TheCalculator was updated to a new version 2017.07- Calcula76.exe.

        The previous have a little problem to solve some simple
        functions as 2*10^x or 2.5*10^x - they dont solve.

        In this version, many results are simplified
        and solutions like literal*k*? are now k*literal*?.
        All other things are the same.

note1:  All upper-case letters are replaced by lower-case letters
              so the solutions are always in lower-case.

note2:  In the file TheCalculator_derivatives15.txt
              we may find 147 examples using almost all functions
              with many different arguments.
       
        Good luck
       

input box=> [(1.2e-1*x^2*sin(x))]'

solution box1=> 0.12*(2*x*sin(x)+x^2*cos(x))

++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [(1.2e1*x^2*sin(x))]'

solution box1=> 12*(2*x*sin(x)+x^2*cos(x))

++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [2*e^x+2*a^x-2*e^-x-2*a^-x]'

solution box1=> 2*e^x+2*ln(a)*a^x+2*e^-x+2*ln(a)*a^-x

++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [2*a^x+2*exp(x)+2*e^x+2*10^x+2*ten(x)+2*ln(x)+2*log(x)+2*sqr(x)+2*sin(x)+2*cos(x)+2*tan(x)+2*cot(x)+2*
sec(x)+2*csc(x)+2*arcsin(x)+2*arccos(x)+2*arctan(x)+2*arccot(x)+2*arcsec(x)+2*arccsc(x)+2*sind(x)+2*cosd(x)+2*tand
(x)+2*cotd(x)+2*secd(x)+2*cscd(x)+2*arcsind(x)+2*arccosd(x)+2*arctand(x)+2*arccotd(x)+2*arcsecd(x)+2*arccscd(x)+2*
sinh(x)+2*cosh(x)+2*tanh(x)+2*coth(x)+2*sech(x)+2*csch(x)+2*arcsinh(x)+2*arccosh(x)+2*arctanh(x)+2*arccoth(x)+2*ar
csech(x)+2*arccsch(x)]'

solution box1=> 2*ln(a)*a^x+2*exp(x)+2*e^x+2*ln(10)*10^x+2*ln(10)*ten(x)+2/x+2/(ln(10)*x)+2/(2*sqr(x))+2*cos(x)-2*
sin(x)+2*sec(x)^2-2*csc(x)^2+2*sec(x)*tan(x)-2*csc(x)*cot(x)+2/sqr(1-x^2)-2/sqr(1-x^2)+2/(1+x^2)-2/(1+x^2)+2/(abs(
x)*sqr(x^2-1))-2/(abs(x)*sqr(x^2-1))+2*cosd(x)-2*sind(x)+2*secd(x)^2-2*cscd(x)^2+2*secd(x)*tand(x)-2*cscd(x)*cotd(
x)+2/sqr(1-x^2)-2/sqr(1-x^2)+2/(1+x^2)-2/(1+x^2)+2/(abs(x)*sqr(x^2-1))-2/(abs(x)*sqr(x^2-1))+2*cosh(x)+2*sinh(x)+2
*sech(x)^2-2*csch(x)^2+2*sech(x)*tanh(x)-2*csch(x)*coth(x)+2/sqr(x^2+1)-2/sqr(x^2-1)+2/(1-x^2)+2/(1-x^2)-2/(x*sqr(
1-x^2))-2/(abs(x)*sqr(1+x^2))

++ 137 +++++++++++++++++++++++++++++++++++++++++++++
input box=> [2.5*a^x+2.5*exp(x)+2.5*e^x+2.5*10^x+2.5*ten(x)+2.5*ln(x)+2.5*log(x)+2.5*sqr(x)+2.5*sin(x)+2.5*cos(x)+
2.5*tan(x)+2.5*cot(x)+2.5*sec(x)+2.5*csc(x)+2.5*arcsin(x)+2.5*arccos(x)+2.5*arctan(x)+2.5*arccot(x)+2.5*arcsec(x)+
2.5*arccsc(x)+2.5*sind(x)+2.5*cosd(x)+2.5*tand(x)+2.5*cotd(x)+2.5*secd(x)+2.5*cscd(x)+2.5*arcsind(x)+2.5*arccosd(x
)+2.5*arctand(x)+2.5*arccotd(x)+2.5*arcsecd(x)+2.5*arccscd(x)+2.5*sinh(x)+2.5*cosh(x)+2.5*tanh(x)+2.5*coth(x)+2.5*
sech(x)+2.5*csch(x)+2.5*arcsinh(x)+2.5*arccosh(x)+2.5*arctanh(x)+2.5*arccoth(x)+2.5*arcsech(x)+2.5*arccsch(x)]'

solution box1=> 2.5*ln(a)*a^x+2.5*exp(x)+2.5*e^x+2.5*ln(10)*10^x+2.5*ln(10)*ten(x)+2.5/x+2.5/(ln(10)*x)+2.5/(2*sqr
(x))+2.5*cos(x)-2.5*sin(x)+2.5*sec(x)^2-2.5*csc(x)^2+2.5*sec(x)*tan(x)-2.5*csc(x)*cot(x)+2.5/sqr(1-x^2)-2.5/sqr(1-
x^2)+2.5/(1+x^2)-2.5/(1+x^2)+2.5/(abs(x)*sqr(x^2-1))-2.5/(abs(x)*sqr(x^2-1))+2.5*cosd(x)-2.5*sind(x)+2.5*secd(x)^2
-2.5*cscd(x)^2+2.5*secd(x)*tand(x)-2.5*cscd(x)*cotd(x)+2.5/sqr(1-x^2)-2.5/sqr(1-x^2)+2.5/(1+x^2)-2.5/(1+x^2)+2.5/(
abs(x)*sqr(x^2-1))-2.5/(abs(x)*sqr(x^2-1))+2.5*cosh(x)+2.5*sinh(x)+2.5*sech(x)^2-2.5*csch(x)^2+2.5*sech(x)*tanh(x)
-2.5*csch(x)*coth(x)+2.5/sqr(x^2+1)-2.5/sqr(x^2-1)+2.5/(1-x^2)+2.5/(1-x^2)-2.5/(x*sqr(1-x^2))-2.5/(abs(x)*sqr(1+x^
2))

++ 138 +++++++++++++++++++++++++++++++++++++++++++++
input box=> [(2/5)*a^x+(2/5)*exp(x)+(2/5)*e^x+(2/5)*10^x+(2/5)*ten(x)+(2/5)*ln(x)+(2/5)*log(x)+(2/5)*sqr(x)+(2/5)*
sin(x)+(2/5)*cos(x)+(2/5)*tan(x)+(2/5)*cot(x)+(2/5)*sec(x)+(2/5)*csc(x)+(2/5)*arcsin(x)+(2/5)*arccos(x)+(2/5)*arct
an(x)+(2/5)*arccot(x)+(2/5)*arcsec(x)+(2/5)*arccsc(x)+(2/5)*sind(x)+(2/5)*cosd(x)+(2/5)*tand(x)+(2/5)*cotd(x)+(2/5
)*secd(x)+(2/5)*cscd(x)+(2/5)*arcsind(x)+(2/5)*arccosd(x)+(2/5)*arctand(x)+(2/5)*arccotd(x)+(2/5)*arcsecd(x)+(2/5)
*arccscd(x)+(2/5)*sinh(x)+(2/5)*cosh(x)+(2/5)*tanh(x)+(2/5)*coth(x)+(2/5)*sech(x)+(2/5)*csch(x)+(2/5)*arcsinh(x)+(
2/5)*arccosh(x)+(2/5)*arctanh(x)+(2/5)*arccoth(x)+(2/5)*arcsech(x)+(2/5)*arccsch(x)]'

solution box1=> 2/5*ln(a)*a^x+(2/5)*exp(x)+(2/5)*e^x+(2/5)*ln(10)*10^x+(2/5)*ln(10)*ten(x)+(2/5)/x+(2/5)/(ln(10)*x
)+(2/5)/(2*sqr(x))+(2/5)*cos(x)+(2/5)*sin(x)+(2/5)*sec(x)^2+(2/5)*csc(x)^2+(2/5)*sec(x)*tan(x)+(2/5)*csc(x)*cot(x)
+(2/5)/sqr(1-x^2)+(2/5)/sqr(1-x^2)+(2/5)/(1+x^2)+(2/5)/(1+x^2)+(2/5)/(abs(x)*sqr(x^2-1))+(2/5)/(abs(x)*sqr(x^2-1))
+(2/5)*cosd(x)+(2/5)*sind(x)+(2/5)*secd(x)^2+(2/5)*cscd(x)^2+(2/5)*secd(x)*tand(x)+(2/5)*cscd(x)*cotd(x)+(2/5)/sqr
(1-x^2)+(2/5)/sqr(1-x^2)+(2/5)/(1+x^2)+(2/5)/(1+x^2)+(2/5)/(abs(x)*sqr(x^2-1))+(2/5)/(abs(x)*sqr(x^2-1))+(2/5)*cos
h(x)+(2/5)*sinh(x)+(2/5)*sech(x)^2+(2/5)*csch(x)^2+(2/5)*sech(x)*tanh(x)+(2/5)*csch(x)*coth(x)+(2/5)/sqr(x^2+1)+(2
/5)/sqr(x^2-1)+(2/5)/(1-x^2)+(2/5)/(1-x^2)+(2/5)/(x*sqr(1-x^2))+(2/5)/(abs(x)*sqr(1+x^2))

[RuiLoureiro]

Hi all,
        This is TheCalculator new powerful version 2017.08- Calcula77.exe.

        In this version, some procedures are improved
        and more results are simplified.

note:   The file TheCalculator_derivatives16.txt show us
           163 examples using almost all functions
           with many different arguments.
       
        Good luck
                                              EDIT: files replaced       
HERE some examples       

Using TheCalculator we get

input box=>     [a^((x-1)/(x+1))]'

solution box1=> ln(a) *2/(x+1)^2* a^((x-1)/(x+1))
++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [10^((x-1)/(x+1))]'

solution box1=> ln(10)*2/(x+1)^2*10^((x-1)/(x+1))    <<<< the same as a^(??)  with a=10

Using Wolframalpha we get

input box=>     [a^((x-1)/(x+1))]'

solution box1=> 2*a^((x-1)/(x+1)) * ln(a)/(x+1)^2  <=> ln(a)*2/(x+1)^2*a^((x-1)/(x+1))

+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [10^((x-1)/(x+1))]'

solution box1=> 10^((x-1)/(x+1)) * (1/(x+1)-(x-1)/(x+1)^2)* ln(10)  <<<- not simplified

HERE some more examples     

input box=> [(a*x+b)*(c*x+d)/((x-1)*(x+1))]'

solution box1=> ((a*(c*x+d)+c*(a*x+b))*((x-1)*(x+1))-(a*x+b)*(c*x+d)*2*x)/((x-1)*(x+1))^2

+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [2*x^(1/3)+3*x^(-1/3)+2*sin(x)^(1/2)+2*cos(x)^(-1/2)]'

solution box1=> 2/3*x^-(2/3)-x^-(4/3)+cos(x)*sin(x)^-(1/2)+sin(x)*cos(x)^-(3/2)

+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [3*x^(1/3)+3*x^(-1/3)+3*sin(x)^(1/2)+3*cos(x)^(-1/2)]'

solution box1=> x^-(2/3)-x^-(4/3)+(3/2)*cos(x)*sin(x)^-(1/2)+(3/2)*sin(x)*cos(x)^-(3/2)

+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [2*x^3-x^3]'

solution box1=> 3*x^2

++ 160 ++++++++++++++++++++++++++++++++++++++++++++
input box=> [(2*x^3-cos(x)-x^3)*sin(x)]'

solution box1=> (6*x^2+sin(x)-3*x^2)*sin(x)+(2*x^3-cos(x)-x^3)*cos(x)

++ 161 ++++++++++++++++++++++++++++++++++++++++++++

input box=> [(2*x^3-cos(arcsin(x^2-x))-x^3)*sin(x)]'

solution box1=> (6*x^2+(2*x-1)/sqr(1-(x^2-x)^2)*sin(arcsin(x^2-x))-3*x^2)*sin(x)+(2*x^3-cos(arcsin(x^2-x))-x^3)*co
s(x)

[RuiLoureiro]

Hi all,
        This is TheCalculator the best powerful version 2017.09- Calcula78.exe.

        In this version, a little problem was corrected, any polynomial is simplified
        (x^128 to x^-128) and more results are simplified.

note:   The file TheCalculator_derivatives17.txt show us
        177 examples using almost all functions
        with many different arguments.
       
        Good luck
:icon14:         
HERE some examples       

input box=> [log(x^-1/b)-log(x^-1/b)+log(-x^-1/b)-log(-x^-1/b)+log(x^-2/b)-log(x^-2/b)+log(-x^-2/b)-log(-x^-2/b)+l
og(x^-3/b)-log(x^-3/b)+log(-x^-3/b)-log(-x^-3/b)]'

solution box1=> -1/(ln(10)*x)+1/(ln(10)*x)-1/(ln(10)*x)+1/(ln(10)*x)-2/(ln(10)*x)+2/(ln(10)*x)-2/(ln(10)*x)+2/(ln(
10)*x)-3/(ln(10)*x)+3/(ln(10)*x)-3/(ln(10)*x)+3/(ln(10)*x)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [log(x^-1/5)-log(x^-1/5)+log(-x^-1/5)-log(-x^-1/5)+log(x^-2/5)-log(x^-2/5)+log(-x^-2/5)-log(-x^-2/5)+l
og(x^-3/5)-log(x^-3/5)+log(-x^-3/5)-log(-x^-3/5)]'

solution box1=> -1/(ln(10)*x)+1/(ln(10)*x)-1/(ln(10)*x)+1/(ln(10)*x)-2/(ln(10)*x)+2/(ln(10)*x)-2/(ln(10)*x)+2/(ln(
10)*x)-3/(ln(10)*x)+3/(ln(10)*x)-3/(ln(10)*x)+3/(ln(10)*x)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [log(x^-5/5)-log(x^-5/5)+log(-x^-5/5)-log(-x^-5/5)+log(x^5/5)-log(x^5/5)+log(-x^5/5)-log(-x^5/5)]'

solution box1=> -5/(ln(10)*x)+5/(ln(10)*x)-5/(ln(10)*x)+5/(ln(10)*x)+5/(ln(10)*x)-5/(ln(10)*x)+5/(ln(10)*x)-5/(ln(
10)*x)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

input box=> [ln(a*x^-1/b)-ln(a*x^-1/b)+ln(-a*x^-1/b)-ln(-a*x^-1/b)+ln(a*x^-2/b)-ln(a*x^-2/b)+ln(-a*x^-2/b)-ln(-a*x
^-2/b)+ln(a*x^-3/b)-ln(a*x^-3/b)+ln(-a*x^-3/b)-ln(-a*x^-3/b)]'

solution box1=> 0
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^128+x^127+x^126+x^125+x^124+x^123+x^122+x^121+x^120+x^119+x^118+x^117+x^116+x^115+x^114+x^113+x^112
+x^111+x^110+x^109+x^108+x^107+x^106+x^105+x^104+x^103+x^102+x^101+x^100-x^128-x^127-x^126-x^125-x^124-x^123-x^122
-x^121-x^120-x^119-x^118-x^117-x^116-x^115-x^114-x^113-x^112-x^111-x^110-x^109-x^108-x^107-x^106-x^105-x^104-x^103
-x^102-x^101-x^100+x]'

solution box1=> 1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^99+x^98+x^97+x^96+x^95+x^94+x^93+x^92+x^91+x^90+x^89+x^88+x^87+x^86+x^85+x^84+x^83+x^82+x^81+x^80+x
^79+x^78+x^77+x^76+x^75+x^74+x^73+x^72+x^71+x^70+x^69+x^68+x^67+x^66+x^65+x^64+x^63+x^62+x^61+x^60+x^59+x^58+x^57+
x^56+x^55+x^54+x^53+x^52+x^51+x^50-x^99-x^98-x^97-x^96-x^95-x^94-x^93-x^92-x^91-x^90-x^89-x^88-x^87-x^86-x^85-x^84
-x^83-x^82-x^81-x^80-x^79-x^78-x^77-x^76-x^75-x^74-x^73-x^72-x^71-x^70-x^69-x^68-x^67-x^66-x^65-x^64-x^63-x^62-x^6
1-x^60-x^59-x^58-x^57-x^56-x^55-x^54-x^53-x^52-x^51-x^50-x]'

solution box1=> -1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^49+x^48+x^47+x^46+x^45+x^44+x^43+x^42+x^41+x^40+x^39+x^38+x^37+x^36+x^35+x^34+x^33+x^32+x^31+x^30+x
^29+x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6
+x^5+x^4+x^3+x^2+x^1+x^0-x^49-x^48-x^47-x^46-x^45-x^44-x^43-x^42-x^41-x^40-x^39-x^38-x^37-x^36-x^35-x^34-x^33-x^32
-x^31-x^30-x^29-x^28-x^27-x^26-x^25-x^24-x^23-x^22-x^21-x^20-x^19-x^18-x^17-x^16-x^15-x^14-x^13-x^12-x^11-x^10-x^9
-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x^1-x^0-x]'

solution box1=> -1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^-49+x^-48+x^-47+x^-46+x^-45+x^-44+x^-43+x^-42+x^-41+x^-40+x^-39+x^-38+x^-37+x^-36+x^-35+x^-34+x^-33
+x^-32+x^-31+x^-30+x^-29+x^-28+x^-27+x^-26+x^-25+x^-24+x^-23+x^-22+x^-21+x^-20+x^-19+x^-18+x^-17+x^-16+x^-15+x^-14
+x^-13+x^-12+x^-11+x^-10+x^-9+x^-8+x^-7+x^-6+x^-5+x^-4+x^-3+x^-2+x^-1+x^-0-x^-49-x^-48-x^-47-x^-46-x^-45-x^-44-x^-
43-x^-42-x^-41-x^-40-x^-39-x^-38-x^-37-x^-36-x^-35-x^-34-x^-33-x^-32-x^-31-x^-30-x^-29-x^-28-x^-27-x^-26-x^-25-x^-
24-x^-23-x^-22-x^-21-x^-20-x^-19-x^-18-x^-17-x^-16-x^-15-x^-14-x^-13-x^-12-x^-11-x^-10-x^-9-x^-8-x^-7-x^-6-x^-5-x^
-4-x^-3-x^-2-x^-1-x^-0-x]'

solution box1=> -1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^-99+x^-98+x^-97+x^-96+x^-95+x^-94+x^-93+x^-92+x^-91+x^-90+x^-89+x^-88+x^-87+x^-86+x^-85+x^-84+x^-83
+x^-82+x^-81+x^-80+x^-79+x^-78+x^-77+x^-76+x^-75+x^-74+x^-73+x^-72+x^-71+x^-70+x^-69+x^-68+x^-67+x^-66+x^-65+x^-64
+x^-63+x^-62+x^-61+x^-60+x^-59+x^-58+x^-57+x^-56+x^-55+x^-54+x^-53+x^-52+x^-51+x^-50-x^-99-x^-98-x^-97-x^-96-x^-95
-x^-94-x^-93-x^-92-x^-91-x^-90-x^-89-x^-88-x^-87-x^-86-x^-85-x^-84-x^-83-x^-82-x^-81-x^-80-x^-79-x^-78-x^-77-x^-76
-x^-75-x^-74-x^-73-x^-72-x^-71-x^-70-x^-69-x^-68-x^-67-x^-66-x^-65-x^-64-x^-63-x^-62-x^-61-x^-60-x^-59-x^-58-x^-57
-x^-56-x^-55-x^-54-x^-53-x^-52-x^-51-x^-50-x]'

solution box1=> -1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [x^-128+x^-127+x^-126+x^-125+x^-124+x^-123+x^-122+x^-121+x^-120+x^-119+x^-118+x^-117+x^-116+x^-115+x^-
114+x^-113+x^-112+x^-111+x^-110+x^-109+x^-108+x^-107+x^-106+x^-105+x^-104+x^-103+x^-102+x^-101+x^-100-x^-128-x^-12
7-x^-126-x^-125-x^-124-x^-123-x^-122-x^-121-x^-120-x^-119-x^-118-x^-117-x^-116-x^-115-x^-114-x^-113-x^-112-x^-111-
x^-110-x^-109-x^-108-x^-107-x^-106-x^-105-x^-104-x^-103-x^-102-x^-101-x^-100+x]'

solution box1=> 1-128*x^-129+128*x^-129

[RuiLoureiro]

Hi all,
        This is TheCalculator the best powerful version 2017.10- Calcula79.exe.

        In this version, a little problem was corrected
        and more results are simplified: multiply
        integer-integer,integer-rational,rational-integer
        and rational-rational.

note:   The file TheCalculator_derivatives19.txt show us
        235 examples using almost all functions
        with many different arguments.
       
        Good luck
       
HERE some examples

input box=>     [sin(3*pi*x)^3                  +cos(3*pi*x)^2]'

solution box1=> 9*pi*cos(3*pi*x)*sin(3*pi*x)^2  -6*pi*sin(3*pi*x)*cos(3*pi*x)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*pi*x)^3                 +cos(-3*pi*x)^2]'

solution box1=> -9*pi*cos(-3*pi*x)*sin(-3*pi*x)^2   +6*pi*sin(-3*pi*x)*cos(-3*pi*x)

++ 210 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*pi*x)^-3                    +cos(-3*pi*x)^-2]'

solution box1=> 9*pi*cos(-3*pi*x)*sin(-3*pi*x)^-4   -6*pi*sin(-3*pi*x)*cos(-3*pi*x)^-3

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*pi*x)^(1/3)                  +cos(-3*pi*x)^(1/3)]'

solution box1=> pi*cos(3*pi*x)*sin(3*pi*x)^-(2/3)   +pi*sin(-3*pi*x)*cos(-3*pi*x)^-(2/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*pi*x)^(-1/3)                 +cos(-3*pi*x)^(-1/3)]'

solution box1=> -pi*cos(3*pi*x)*sin(3*pi*x)^-(4/3)  -pi*sin(-3*pi*x)*cos(-3*pi*x)^-(4/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*pi*x)^(-1/3)                +cos(-3*pi*x)^(-1/3)]'

solution box1=> pi*cos(-3*pi*x)*sin(-3*pi*x)^-(4/3) -pi*sin(-3*pi*x)*cos(-3*pi*x)^-(4/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*pi*x)^(1/3)
                +cos(-3*pi*x)^(1/3)                 -sin(3*pi*x)^(1/3)]'

solution box1=> pi*cos(3*pi*x)*sin(3*pi*x)^-(2/3)
               +pi*sin(-3*pi*x)*cos(-3*pi*x)^-(2/3) -pi*cos(3*pi*x)*sin(3*pi*x)^-(2/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*a*x)^-3                  +cos(3*b*x)^-2]'

solution box1=> -9*a*cos(3*a*x)*sin(3*a*x)^-4   +6*b*sin(3*b*x)*cos(3*b*x)^-3

++ 220 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*a*x)^-3                 +cos(-3*b*x)^-2]'

solution box1=> 9*a*cos(-3*a*x)*sin(-3*a*x)^-4  -6*b*sin(-3*b*x)*cos(-3*b*x)^-3

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*a*x)^(1/3)               +cos(-3*a*x)^(1/3)]'

solution box1=> a*cos(3*a*x)*sin(3*a*x)^-(2/3)  +a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*a*x)^(-1/3)              +cos(-3*a*x)^(-1/3)]'

solution box1=> -a*cos(3*a*x)*sin(3*a*x)^-(4/3) -a*sin(-3*a*x)*cos(-3*a*x)^-(4/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*a*x)^(-1/3)                 +cos(-3*a*x)^(-1/3)]'

solution box1=> a*cos(-3*a*x)*sin(-3*a*x)^-(4/3)    -a*sin(-3*a*x)*cos(-3*a*x)^-(4/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(3*a*x)^(1/3)   
                +cos(-3*a*x)^(1/3)                  -sin(3*a*x)^(1/3)]'

solution box1=> a*cos(3*a*x)*sin(3*a*x)^-(2/3) 
               +a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)    -a*cos(3*a*x)*sin(3*a*x)^-(2/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [cos(-3*a*x)^(1/3)                  -sin(3*a*x)^(1/3)]'

solution box1=> a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)    -a*cos(3*a*x)*sin(3*a*x)^-(2/3)

+++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [cos(-3*a*x)^(1/3)                  +sin(3*a*x)^(1/3)]'

solution box1=> a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)    +a*cos(3*a*x)*sin(3*a*x)^-(2/3)

++ 227 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [cos(-3*a*x)^(1/3)                  +cos(3*a*x)^(1/3)]'

solution box1=> a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)    -a*sin(3*a*x)*cos(3*a*x)^-(2/3)

++ 228 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [cos(-3*a*x)^(1/3)                  -cos(3*a*x)^(1/3)]'

solution box1=> a*sin(-3*a*x)*cos(-3*a*x)^-(2/3)    +a*sin(3*a*x)*cos(3*a*x)^-(2/3)

++ 229 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [x      +cos(3*a*x)^(1/3)]'

solution box1=> 1       -a*sin(3*a*x)*cos(3*a*x)^-(2/3)

++ 230 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [cos(-3*a*x)^(4/3)                  -cos(3*a*x)^(2/3)]'

solution box1=> 4*a*sin(-3*a*x)*cos(-3*a*x)^(1/3)   +2*a*sin(3*a*x)*cos(3*a*x)^-(1/3)

++ 231 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(-3*pi*x+a)^(-1/3)                      +cos(-3*pi*x+b)^(-1/3)]'

solution box1=> pi*cos(-3*pi*x+a)*sin(-3*pi*x+a)^-(4/3)     -pi*sin(-3*pi*x+b)*cos(-3*pi*x+b)^-(4/3)

++ 232 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(a-3*pi*x)^(-1/3)                       +cos(b-3*pi*x)^(-1/3)]'

solution box1=> pi*cos(a-3*pi*x)*sin(a-3*pi*x)^-(4/3)       -pi*sin(b-3*pi*x)*cos(b-3*pi*x)^-(4/3)

++ 233 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin(a-(2/3)*pi*x)^3                +cos(b-(3/2)*pi*x)^2
                -sin(a-(2/3)*pi*x)^(1/3)            -cos(b-(3/2)*pi*x)^(1/2)]'

solution box1=> -2*pi*cos(a-(2/3)*pi*x)*sin(a-(2/3)*pi*x)^2
                +3*pi*sin(b-(3/2)*pi*x)*cos(b-(3/2)*pi*x)

                +(2/9)*pi*cos(a-(2/3)*pi*x)*sin(a-(2/3)*pi*x)^-(2/3)
                -(3/4)*pi*sin(b-(3/2)*pi*x)*cos(b-(3/2)*pi*x)^-(1/2)

++ 234 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin((2/3)*pi*x)^3                  +cos((3/2)*pi*x)^2
                -sin((2/3)*pi*x)^(1/3)              -cos((3/2)*pi*x)^(1/2)]'

solution box1=> 2*pi*cos((2/3)*pi*x)*sin((2/3)*pi*x)^2
               -3*pi*sin((3/2)*pi*x)*cos((3/2)*pi*x)

               -(2/9)*pi*cos((2/3)*pi*x)*sin((2/3)*pi*x)^-(2/3)
               +(3/4)*pi*sin((3/2)*pi*x)*cos((3/2)*pi*x)^-(1/2)

++ 235 ++++++++++++++++++++++++++++++++++++++++++
input box=>     [sin((2/3)*a*x)^3                   +cos((3/2)*a*x)^2
                -sin((2/3)*a*x)^(1/3)               -cos((3/2)*a*x)^(1/2)]'

solution box1=> 2*a*cos((2/3)*a*x)*sin((2/3)*a*x)^2
                -3*a*sin((3/2)*a*x)*cos((3/2)*a*x)

                -(2/9)*a*cos((2/3)*a*x)*sin((2/3)*a*x)^-(2/3)
                +(3/4)*a*sin((3/2)*a*x)*cos((3/2)*a*x)^-(1/2)

[RuiLoureiro]

Hi all,
        TheCalculator was updated.
        The new best powerful version is 2017.11 -Calcula80.exe.       

        The file TheCalculator_derivatives22.txt show us 257 examples.
       
        Good luck

HERE some examples

input box=>     [ln(a*x)-ln(a*x)+ln(-a*x)-ln(-a*x)]'

solution box1=> 0
+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [ln(3*a*x)-ln(3*a*x)+ln(-3*a*x)-ln(-3*a*x)]'

solution box1=> 0
+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=>     [ln(pi*x)-ln(pi*x)+ln(-pi*x)-ln(-pi*x)]'

solution box1=> 0
+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*pi*x)-ln(3*pi*x)+ln(-3*pi*x)-ln(-3*pi*x)]'

solution box1=> 0
+++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [log(a*x)-log(a*x)+log(-a*x)-log(-a*x)+log(3*a*x)-log(3*a*x)+log(-3*a*x)-log(-3*a*x)
+log(pi*x)-log(pi*x)+log(-pi*x)-log(-pi*x)+log(3*pi*x)-log(3*pi*x)+log(-3*pi*x)-log(-3*pi*x)]'

solution box1=> 0
++ 256 ++++++++++++++++++++++++++++++++++++++++++++
input box=>     [ln(3*a*x^2+b)]'

solution box1=> 6*a*x/(3*a*x^2+b)
++ 257 ++++++++++++++++++++++++++++++++++++++++++++
input box=>     [log(3*a*x^2+b)]'

solution box1=> 6*a*x/(ln(10)*(3*a*x^2+b))

[RuiLoureiro]

Hi all,
        TheCalculator was updated.
        The new best powerful version is 2017.12 -Calcula81.exe.       

        The file TheCalculator_derivatives24.txt show us 270 examples.
       
        Good luck

HERE SOME EXAMPLES       

input box=> [ln(3*a/x^-1)+ln(3*a*x^-1)]'

solution box1=> 0

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^-1)]'

solution box1=> x^-1

++ 260 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^-2)]'

solution box1=> 2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^2)]'

solution box1=> -2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a*x^-2)]'

solution box1=> -2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a*x^2)]'

solution box1=> 2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^-20)]'

solution box1=> 20*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^-2)]'

solution box1=> 2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(30*a/x^-2)]'

solution box1=> 2*x^-1

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(30*a/x^-20)]'

solution box1=> 20*x^-1

++ 268 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a/x^-20)+ln(3*a/x^-2)+ln(30*a/x^-20)+ln(30*a/x^-2)]'

solution box1=> 44*x^-1

++ 269 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(3*a*x^20)]'

solution box1=> 20*x^-1

++ 270 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
input box=> [ln(30*a/x^-20)+ln(30*a*x^-20)]'

solution box1=> 0