Chapter 4.5, Problem 245E

For the following exercises, find $\frac{dy}{dx}$ using partial derivatives.

245. If $z=xy{e}^{x/y},x=r\cos \theta$ , and $y=r\sin \theta$ , find $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial v}$ when $r=2$ and $\theta =\frac{\pi }{6}$ .