Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.5 - Implicit Differentiation - 3.5 Exercises: 14

Answer

$y' = \frac{1+y-e^{y}cos(x)}{e^{y}sin(x)-x}$

Work Step by Step

Start with equation: $e^{y}sin(x) = x+xy$. Differentiate Both Sides: $e^{y}y'sin(x)+e^{y}cos(x)=1+xy'+y$. Solve for y': $y'(e^{y}sin(x)-x) = 1+y-e^{y}cos(x)$. $y' = \frac{1+y-e^{y}cos(x)}{e^{y}sin(x)-x}$
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