Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.4 - The Chain Rule - Exercises 14.4 - Page 817: 36



Work Step by Step

Consider $\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\dfrac{\partial y}{\partial u}$ and $(y\cos xy+\sin y)(2u)+(x \cos xy+x\cos y)(v)=((uv)\cos (u^3v+uv^3)+\sin (uv))(2u)+((u^2+v^2) \cos (u^3v+uv^3)+(u^2+v^2)\cos (uv))(v)$ For the point, $u=0,v=1$: Thus, $\dfrac{\partial w}{\partial v}=[(1)\cos (0+0)+\sin (0)](0)+((0+1) \cos (0)+(0+1)\cos (0))(1)$ or, $0+1+1=2$
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