Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Practice Exercises - Page 865: 34


$$\frac{\partial w}{\partial x}-5 \frac{\partial w}{\partial y}=0$$

Work Step by Step

Given $$w=f(s),\ \ \ \ \ s= y+5x$$ Since \begin{align*} \frac{\partial w}{\partial x}&=\frac{\partial w}{\partial s}\frac{\partial s}{\partial x}= 5\frac{\partial w}{\partial s}\\ \frac{\partial w}{\partial y}&=\frac{\partial w}{\partial s}\frac{\partial s}{\partial y}=\frac{\partial w}{\partial s} \end{align*} Then \begin{align*} \frac{\partial w}{\partial x}-5 \frac{\partial w}{\partial y}&= 5\frac{\partial w}{\partial s}-5\frac{\partial w}{\partial s}\\ &=0 \end{align*}
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