Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 42


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

Work Step by Step

Given $$xe^y= y- 1$$ Differentiate with respect to $x$ \begin{align*} xe^yy'+e^y&= y'\\ (xe^y-1)y'&=-e^y\\ y'&=\frac{e^y}{1-xe^y} \end{align*}
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