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 782: 65


$$ f_{uuv}= 2v\sin(u+v^2).$$

Work Step by Step

Since $ f(u,v)=\cos(u+v^2)$, then using the chain rule, we have $$ f_u=-\sin(u+v^2), \quad f_{uu}=-\cos(u+v^2).$$ Then, we have $$ f_{uuv}=\sin(u+v^2)(2v)=2v\sin(u+v^2).$$
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