Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 453: 42

$(2x+1)e^{-1/x}$

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