Chapter 4.7, Problem 7P

If $x=r\cos \theta$ and $y=r\sin \theta ,$ find ${(\partial y/\partial \theta )}_r$ and ${(\partial y/\partial \theta )}_x.$ Also find ${(\partial \theta /\partial y)}_x$ in two ways (by eliminating $r$ from the given equations and then differentiating, or by taking differentials in both equations and then eliminating dr). When are $\partial y/\partial \theta$ and $\partial \theta /\partial y$ reciprocals?