University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.3 - Partial Derivatives - Exercises - Page 702: 38

Answer

$g_r=1-\cos \theta ; \\ g_θ=r \space \sin \theta ; \\g_z=-1$

Work Step by Step

Our aim is to take the first partial derivative of the given function $g(x,y)$ with respect to $r$, by keeping $z$ and $\theta$ as constants: $g_r=1-\cos \theta$ Now, we repeat the process for the other partial derivatives: $g_θ=r \space \sin \theta$ $\\g_z=-1$
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