Answer
$\frac{dy}{dx}=(2(x+1)e^{\frac{-2}{x}})$
Work Step by Step
$y=x^2e^{\frac{-2}{x}}$
on differentiating both sides:
$\frac{dy}{dx}=\frac{d(x^2e^{\frac{-2}{x}})}{dx}$
$\frac{dy}{dx}=2xe^{\frac{-2}{x}}+(x^2(\frac{2}{x^2})e^{\frac{-2}{x}})$
$\frac{dy}{dx}=(2(x+1)e^{\frac{-2}{x}})$
