Answer
${dy}=(1-x)e^{(-x)}{dx}$
Work Step by Step
We evaluate the function: $y=xe^{-{x}}$
on differentiating the above:
$\frac{dy}{dx}=\frac{d{(xe^{(-x)})}}{dx}$
on applying the product rule:
$\frac{dy}{dx}=e^{-x}{\frac{dx}{dx}}+x{\frac{de^{(-x)}}{dx}}$
or $\frac{dy}{dx}=e^{(-x)}-xe^{(-x)}$
or ${dy}=(e^{(-x)}-xe^{(-x)}){dx}$
or${dy}=(1-x)e^{(-x)}{dx}$
The final answer is: ${dy}=(1-x)e^{(-x)}{dx}$
