Answer
$(2x+1)e^{-1/x}$
Work Step by Step
$\frac{d}{dx}x^2e^{-1/x}$
$=x^2\frac{d}{dx}e^{-1/x}+e^{-1/x}\frac{d}{dx}x^2$
$=x^2e^{-1/x}\frac{d}{dx}(-\frac{1}{x})+e^{-1/x}*2x$
$=x^2e^{-1/x}*\frac{1}{x^2}+e^{-1/x}*2x$
$=e^{-1/x}+e^{-1/x}*2x$
$=(2x+1)e^{-1/x}$