Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Section 16.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises 16.2 - Page 955: 2


$\nabla f (x, y, z)=\dfrac{1}{(x^2+y^2+z^2)} (xi+yj+zk)$

Work Step by Step

Re-write as: $f(x,y,z)=\dfrac{1}{2} \ln (x^2+y^2+z^2)$ Thus, the gradient field can be computed as $\nabla f (x, y, z)=\dfrac{1}{2} [\dfrac{2x}{(x^2+y^2+z^2)}i +\dfrac{2y}{(x^2+y^2+z^2)} j +\dfrac{2z}{(x^2+y^2+z^2)} k ]$ or, $\nabla f (x, y, z)=\dfrac{1}{(x^2+y^2+z^2)} (xi+yj+zk)$
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