4344 Let r = xi + y j + zk, let r = r, let f be a differentiablefunction of one

Chapter 15, Problem 43

(choose chapter or problem)

Let \(r = xi + y j + zk\), let \(r\) = || r ||, let \(f\) be a differentiable function of one variable, and let F(r) = \(f(r)\)r.

(a) Use the chain rule and Exercise 41(b) to show that

                                                 \(\nabla f(r)=\frac{f^{\prime}(r)}{r}\)

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

Equation Transcription:

∇

Text Transcription:

xi + yj + zk

r

f

f(r)

nabla f(r) = frac{f’(r)}{r}

f(r)  +  rf’(r)