I am having some difficulty with a few problems which seem to be similar in a sense. One of these problems is:

Suppose z = f(x,y) has continuous partial derivatives. Let:

$\displaystyle x = e^r\cos\theta, y = e^r\sin\theta$ Show that then:

$\displaystyle (\frac{\partial z}{\partial x})^2+ (\frac{\partial z}{\partial y})^2 = e^{-2r}(( \frac{\partial z}{\partial r})^2 + (\frac{\partial z}{\partial \theta})^2)$

I am fairly lost at how to begin this. I know I could find the partial of x with respect to r or theta, but I don't know how to tie it into the question. I was absent during that class, and the book doesn't go through a problem similar to it either. Thanks for any help.