Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 13 - Partial Derivatives - 13.1 Functions Of Two Or More Variables - Exercises Set 13.1: 4

Answer

(a) $g(x/y)=\frac{x}{y}\sin\left(\frac{x}{y}\right)$, (b) $g(xy)=xy\sin(xy)$, (c) $g(x-y)=(x-y)\sin(x-y)$

Work Step by Step

(a) Substitute $x=x/y$: $$g(x/y)=\frac{x}{y}\sin\left(\frac{x}{y}\right)$$ (b) Substitute $x=xy$: $$g(xy)=xy\sin(xy)$$ (c) Substitute $x=x-y$: $$g(x-y)=(x-y)\sin(x-y)$$
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