## Calculus: Early Transcendentals 8th Edition

$\frac{e^{y}}{1-xe^{y}}$
Start with the function $xe^{y}=y-1$. Differentiate both sides of the equation: $e^{y}+xe^{y}y'=y'$. Consolidate y' terms and factor out y': $e^{y}=y'(1-xe^{y})$. Divide by $1-xe^{y}$ to arrive at the answer: $\frac{e^{y}}{1-xe^{y}}$.