Chapter 9, Problem 17P

The product rule can be applied to the divergence to the divergence of scalar f times vector $\stackrel{\to }{G}$ as: $\stackrel{\to }{\nabla }\cdot \left(f\stackrel{\to }{G}\right)=\stackrel{\to }{G}\cdot \stackrel{\to }{\nabla }f+d\stackrel{\to }{\nabla }.\stackrel{\to }{G}$ . Expand both sides of this equation in Cartesian coordinates and verify that it is correct.