Chapter 1.4, Problem 235E

For the following exercises, find the slope of a tangent line to a polar curve $r=f\left(\theta \right)$ . Let $x=r\cos \theta =f\left(\theta \right)\cos \theta$ and $y=r\sin \theta =f\left(\theta \right)\sin \theta$ , so the polar equation $r=f\left(\theta \right)$ is now written in parametric form.

235. Use the de?nition of the derivative $\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }$ and the product rule to derive the derivative of a polar equation.