Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Review - Exercises: 8

Answer

$\dfrac {y\cos x-e^{y}}{xe^{y}-\sin x}$

Work Step by Step

$xe^{y}=y\sin x\Rightarrow \dfrac {d}{dx}\left( xe^{y}\right) =\dfrac {d}{dx}\left( y\sin x\right) \Rightarrow e^{y}+xe^{y}\dfrac {dy}{dx}=\dfrac {dy}{dx}\sin x+y\cos x\Rightarrow \dfrac {dy}{dx}=\dfrac {y\cos x-e^{y}}{xe^{y}-\sin x}$
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