Chapter 12, Problem 7PS

To determine

To prove: If $r\left(t\right)$ is a nonzero differential function of $t$, then $\frac{d}{dt}\left[\Vert r\left(t\right)\Vert \right]=\frac{r\left(t\right)·r^{\prime }\left(t\right)}{\Vert r\left(t\right)\Vert }$.