Chain rule with symbolic toolbox

Hello,

I'm trying to derive a symbolic function that is a function of another symbolic function. Say that I have a function x that is an unspecified function x=x(y(theta)). I'd like to take the derivative of x with respect to theta: dx/dtheta=dx/dy * dy/dtheta

In Matlab I write

syms theta y(theta);
x=sym('x(y(theta))');
diff(x,theta)

The answer I get is 0. I really cannot figure out what is wrong with the code. Any help is greatly appreciated. Thanks!

Answer 1

[Star Strider]

This:

syms theta y(theta) x(y)
x = x(y)
Dyt = diff(y,theta)
Dxt = diff(x,theta)

produces:

x =

      x(y(theta))

Dyt(theta) =

      D(y)(theta)

Dxt =

      D(x)(y(theta))*diff(y(theta), theta)

Is that what you wanted?

[Nicola]

Thanks, this works!

[Star Strider]

My pleasure!

[Mr.Gh]

I am trying to find the derivative of "A" with respect to "a", but I get some errors:

syms t a(t) b(t) A(a,b)
A = a^2 + b^2;
B = formula(A);
aS = formula(a);
D_A_t = diff(B,aS);

error:

Error using sym/diff (line 70)

Second argument must be a variable or a nonnegative integer

specifying the number of differentiations.

Error in (line 5)

D_A_t = diff(B,aS);

Please advise.

[Star Strider]

Post this as a new Question. Much has changed in the last 6 years. Be sure to mention the version/release of MATLAB that you are using.

[Meet Mevada]

Thanks man.This helped me a lot.

[Star Strider]

Meet Mevada — My pleasure!