Chapter 14.5, Problem 65E

Properties of div and curl Prove the following properties of the divergence and curl. Assume F and G are differentiable vector fields and c is a real number.

a.     $\nabla \cdot \left(F+G\right)=\nabla \cdot F+\nabla \cdot G$

b.     $\nabla \times \left(F+G\right)=\left(\nabla \times F\right)+\left(\nabla \times G\right)$

c.     $\nabla \cdot \left(cF\right)=c\left(\nabla \cdot F\right)$

d.     $\nabla \times \left(cF\right)=c\left(\nabla \times F\right)$