Chapter 14.5, Problem 67E

Identities Prove the following identities. Assume that φ is a differentiable scalar-valued function and F and G are differentiable vector fields, all defined on a region of R³.

67.     $\nabla \cdot \left(\phi F\right)=\nabla \phi \cdot F+\phi \nabla \cdot F$ (Product Rule)