Chapter 13.2, Problem 57E

To determine

To show: The expression $\frac{d}{dt}\left|\text{r}\left(t\right)\right|$ is equals to the expression $\frac{1}{\left|\text{r}\left(t\right)\right|}\text{r}\left(t\right)\cdot \text{r}\prime \left(t\right)$ when the vector $\text{r}\left(t\right)\ne 0$.