Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 38


$g_r=1-cosθ$ $g_θ=rsinθ$ $g_z=-1$

Work Step by Step

Take the first partial derivatives of the given function. When taking a partial derivative with respect to r, treat θ and z as constants, with respect to θ, treat r and z as constants, and with respect to z, treat r and θ as constants: $g_r=1-cosθ$ $g_θ=rsinθ$ $g_z=-1$
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