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: 25

Answer

$g_u=10uv(u^2v-v^3)^4$, $g_v=5(u^2-3v^2)(u^2v-v^3)^4$.

Work Step by Step

$g(u,v)=(u^2v-v^3)^5$ In order to find $g_u$ we treat $v$ as a constant and differentiate with respect to $u$. $g_u=10uv(u^2v-v^3)^4$ In order to find $g_v$ we treat $u$ as a constant and differentiate with respect to $v$. $g_v=5(u^2-3v^2)(u^2v-v^3)^4$
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