Answer
$$y' =\frac{e^y}{1-xe^y}$$
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*}
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 42
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