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: 10

Answer

$y' = \frac{1 - e^y}{xe^y + 1}$

Work Step by Step

$xe^y = x - y$ use the product rule on $xe^y$ and differentiate both sides $(x)(y'e^y) + (1)(e^y) = 1 - y'$ $xy'e^y + y' = 1 - e^y$ $y'(xe^y + 1) = 1 - e^y$ $y' = \frac{1 - e^y}{xe^y + 1}$
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