Chapter 12.6, Problem 2E

To determine

To prove:

For $x=r\cos \theta$ and $y=r\sin \theta$,

$r\frac{dr}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}$ …$(1)$

$r^2\frac{d\theta }{dt}=x\frac{dy}{dt}-y\frac{dx}{dt}$. …$(2)$