Answer
$\frac{e^{y}}{1-xe^{y}}$
Work Step by Step
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: $\frac{e^{y}}{1-xe^{y}}$.
