Chapter 15.1, Problem 43ES

$\text{Let}\text{r}=x\text{i}+y\text{j}+z\text{k,}\text{let }r=‖\text{r}‖,\text{let}f$ be a differentiable function of one variable, and let $\text{F(r)}=f(r)\text{r}\text{.}$

(a) Use the chain rule and Exercise 41(b) to show that $\nabla f(r)=\frac{f\text{'}(r)}{r}\text{r}$

(b) Use the result in part (a) and Exercises 35 and 42 (a) to show that div $\text{F}=3f(r)+rf\text{'}(r).$