Derivate of composition of vector functions

Question

I have troubles to find derivate of composition of two vector functions:$f(x,y)=(x^2,y^2), g(a,b)=(a\cos b,a\sin b)$ where $a>0, b\in(0,2\pi)$. So i need to find $d(f o g)$. I am not even sure what formula to use, so any link on already done examples or explanation would be helpful.

Answer 1

We have

$$(f \circ g)(a,b)= (a^2 \cos^2 b, a^2 \sin^2 b).$$

Now compute the Jacobian matrix of $f \circ g.$