Chapter 15.1, Problem 44ES

(a) Use part (a) of Exercise 43, Exercise 36, and Exercise 41(a) to show that curl $\text{F}\text{=}\text{0}\text{.}$

(b) Use the result in part (a) of Exercise 43 and Exercise 35 and 42 (a) to show that

${\nabla }^{2}f(r)=2\frac{f^{\prime }(r)}{r}+f^{″}(r)$