Section 14.5 Chain Rule

Assume that all the given functions have continuous second-order partial derivatives. If \(z = f(x, y)\), where \(x = r \cos \theta\) and \(y = r \sin \theta\), find (a) \(\partial z/\partial r\), (b) \(\partial z/\partial \theta\), and (c) \(\partial^2 z/\partial r \partial \theta\).