How can I derivate a function with respect to another function with "mathematica" or "matlab"?

Question

for example:

y=x^2; dy/dx=2x;

v=2 x^3; dv/dx= 6 x^2 [not zero!!!!]

but dv/dy=3x;

and don't preach me to do it by my hand, it's an example and i have a very complicated equation to solve.

Answer 1

Go to class and figure it out!!

Answer 2

3 + 3 = 5

GO DIEGO GO!

Answer 3

As usual, you have some people here who don't know how to read and don't know what you are talking about.  Time for a serious answer.

First of all, are you trying to differentiate numerically or symbolically?  The examples you gave are all symbolic differentiation and for this Mathematica will be the best.  You cannot do symbolic differentiation in MATLAB.

If you are working numerically (such as trying to work with a function for which you only have a data table just trying to approximate the slope of a tangent line) then MATLAB will be the best.  You can do numerical stuff in Mathematica but I still prefer MATLAB.  It is much easier to use for numerical calculations.

Now, assuming that you want to work symbolically, then, as far as I know, there is not way on Mathematica to differentiate a function with respect to another function.  So the way I would do it (the obvious way) would be to differentiate both functions with respect to the same variable and divide the two derivatives and simplify.

Using your example, find dy/dx and dv/dx and then in order to get dv/dy just simplify (dv/dx)/(dy/dx).

If you need specific help or the commands on how to do this, feel free to send me a message.