Chapter 14.5, Problem 68E

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.

68.     $\nabla \times \left(\phi F\right)=\left(\nabla \phi \times F\right)+\left(\phi \nabla \times F\right)$ (Product Rule)