University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 13 - Practice Exercises - Page 749: 19

Answer

$\cos \theta+ \sin \theta$ and $r(-\sin \theta+\cos \theta)$

Work Step by Step

Given: $g=r \cos \theta+ r \sin \theta$ Now, $\dfrac{\partial g}{\partial \theta}=\dfrac{\partial }{\partial r} [r \cos \theta+ r \sin \theta]=\dfrac{\partial r}{\partial r} [\cos \theta+ \sin \theta]=\cos \theta+ \sin \theta$ and $\dfrac{\partial g}{\partial \theta}=\dfrac{\partial }{\partial \theta} [r \cos \theta+ r \sin \theta]=r(-\sin \theta+\cos \theta)$ Hence, $\cos \theta+ \sin \theta$ and $r(-\sin \theta+\cos \theta)$
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