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: 69


$$ F_{uu\theta} =2\theta v^2\cosh (uv+\theta^2).$$

Work Step by Step

Since $ F(u,v,\theta)=\sinh (uv+\theta^2)$, then using the chain rule, we have $$ F_{u}=\cosh (uv+\theta^2) (v)=v\cosh (uv+\theta^2),$$ $$ F_{uu}=v\sinh(uv+\theta^2) (v)=v^2\sinh(uv+\theta^2),$$ $$ F_{uu\theta}= v^2\cosh (uv+\theta^2)(2\theta)=2\theta v^2\cosh (uv+\theta^2).$$
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