Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 22


$$ z_u= \cos (u^2v) (2uv) = 2uv \cos (u^2v), \quad \\ z_v= \cos (u^2v) (u^2) = u^2\cos (u^2v). $$

Work Step by Step

Recall that $(\sin x)'=\cos x$. Recall that $(x^n)'=nx^{n-1}$ Since $ z=\sin (u^2v)$, then we have $$ z_u= \cos (u^2v) (2uv) = 2uv \cos (u^2v), \quad\\ z_v= \cos (u^2v) (u^2) = u^2\cos (u^2v). $$
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