Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.3 - Partial Derivatives - 14.3 Exercise - Page 924: 20

Answer

$z_x=\sin{(xy)}+xy\cos{(xy)}$, $z_y=x^2\cos{(xy)}$.

Work Step by Step

$z=x\sin{(xy)}$ In order to find $z_x$ we treat $y$ as a constant and differentiate with respect to $x$. $z_x=\sin{(xy)}+xy\cos{(xy)}$ In order to find $z_y$ we treat $x$ as a constant and differentiate with respect to $y$. $z_y=x^2\cos{(xy)}$
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