The question is

Let $\displaystyle z=f(x,y)$ be a differential function of x and y and let x=rcosθ and y=rsinθ

Show that $\displaystyle (\frac{\partial z}{\partial x})^2+(\frac{\partial z}{\partial y})^2=(\frac{\partial z}{\partial r})^2+\frac{1}{r^2}(\frac{\partial z}{\partial \theta})^2$