Find $\frac{d y}{d x}$ by implicit differentiation. \[ x e^{y}=x-y \]

Step 1 ：Differentiate both sides of the equation \(xe^y = x - y\) with respect to \(x\).

Step 2 ：On the left side, use the product rule of differentiation to get \(e^y + xye^y\).

Step 3 ：On the right side, the derivative of \(x\) with respect to \(x\) is 1 and the derivative of \(-y\) with respect to \(x\) is \(-\frac{dy}{dx}\).

Step 4 ：So, the differentiated equation is \(e^y + xye^y = 1 - \frac{dy}{dx}\).

Step 5 ：Rearrange the equation to isolate \(\frac{dy}{dx}\) on one side to get \(\frac{dy}{dx} = e^y + xye^y - 1\).

Step 6 ：So, the derivative of \(y\) with respect to \(x\) is \(\boxed{\frac{dy}{dx} = e^y(1 + xy) - 1}\).