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: 4


$\nabla g(x,y,z)=(y+z) i +(x+z) j +(y+x) k$

Work Step by Step

Re-write as: $ g(x,y,z)=xy+yz+xz$ The gradient field of $f(x,y,z)$ can be computed as: $\nabla f(x,y,z) =\dfrac{\partial (f(x,y,z))}{\partial x} i+\dfrac{\partial (f(x,y,z))}{\partial y} j+\dfrac{\partial (f(x,y,z))}{\partial z}k $ Thus, the gradient is: $\nabla g(x,y,z)=(y+z) i +(x+z) j +(y+x) k$
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