Chapter 12.2, Problem 67E

To determine

To prove: $\frac{d}{dt}\left\{r\left(t\right).\left[u\left(t\right)\times v(t)\right]\right\}=r\text{'}\left(t\right).\left[u\left(t\right)\times v\left(t\right)\right]+r\left(t\right).\left[u\text{'}\left(t\right)\times v\left(t\right)\right]+r\left(t\right).\left[u\left(t\right)\times v\text{'}\left(t\right)\right]$