Use the transformations relating polar and Cartesian coordinates to prove that [frac{d theta}{d t}=frac{1}{r^{2}}left[x frac{d y}{d t}-y frac{d x}{d t} ight]]

Use the transformations relating polar and Cartesian coordinates to prove that

\[\frac{d \theta}{d t}=\frac{1}{r^{2}}\left[x \frac{d y}{d t}-y \frac{d x}{d t}\right]\]