How to differentiate, then define a variable and integrate with respect to a different variable?

Dear community,

I'd like to create a function file in which I firstly differentiate a function Psi with respect to z. After differentiation, z is defined and becomes a function of x. The result shall then be integrated with resprect to x. So, something like

F=int(dPsi(x,z(x))/dz)dx

How do I do it in matlab? In mudpad, maple etc. it's obviously easy but I get stuck in Matlab because firstly, my symbolic z is a variable and then a function.

Any help is very appreciated.

Kind regards

[Bruno Pop-Stefanov]

If you have an expression in MuPAD which does the differentiation then the integration, you can import it into MATLAB as a symbolic expression.

The following example page explains how to copy variables and expressions between MATLAB and MuPAD:

http://www.mathworks.com/help/symbolic/copy-variables-and-expressions-between-matlab-and-mupad.html

[Magnus]

Yes, sure. Thanks. But I though of doing it all in one function to allow for changes in the function z(x) without doing mupad processing again.

Answer 1

[Bruno Pop-Stefanov]

I wrote a small example below and everything seems to work fine.

1. Define the function Psi

    syms y
    Psi(y) = 1 + y^2;

2. Differentiate it

    dPsi = diff(Psi);

3. Define the z-function of x

    syms x
    z(x) = 1/x;

4. Integrate dPsi of z with respect to x

    F = int(dPsi(z),x)

F =

2*log(x)

[Magnus]

ok, so a change of variables handle is the solution. Thanks, Bruno.