Section 13.2: Derivatives and Integrals of Vector Functions

If \(\mathbf{r}(t) \neq \mathbf{0}\), show that \(\frac{d}{dt}|\mathbf{r}(t)| = \frac{1}{|\mathbf{r}(t)|}\mathbf{r}(t) \cdot \mathbf{r}'(t)\). [Hint: \(|\mathbf{r}(t)|^2 = \mathbf{r}(t) \cdot \mathbf{r}(t)\)]