Chapter 12.3, Problem 55E

To determine

To show:That a polar curve $r=f(\theta )$ has parametric equations $x=f(\theta )\cos \theta$, $y=f(\theta )\sin \theta$ And then prove $\frac{dy}{dx}=\frac{f(\theta )\cos \theta +f\text{'}(\theta )\sin \theta }{-f(\theta )\sin \theta +f\text{'}(\theta )\cos \theta }$