Chapter 12.2, Problem 54ES

Let $\text{u}=\text{u}\left(t\right),\text{v}=\text{v}\left(t\right),\text{and}\text{w}=\text{w}\left(t\right)$ be differentiable vector-values functions. Use formulas (6) and (7) to show that $\frac{d}{dt}\left[\text{u}\cdot \left(\text{v}\times \text{w}\right)\right]=\frac{d\text{u}}{dt}\cdot \left[\text{v}\times \text{w}\right]+\text{u}\cdot \left[\frac{d\text{v}}{dt}\times \text{w}\right]+\text{u}\cdot \left[\text{v}\times \frac{d\text{w}}{dt}\right]$