What is (d^2}{dx^2}(xe^{-\frac{x^2)/2}) ?

The answer to (d^2}{dx^2}(xe^{-\frac{x^2)/2}) is e^{-(x^2)/2}x^3-3e^{-(x^2)/2}x

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(d^2}{dx^2}(xe^{-\frac{x^2)/2})

\frac{d ^{2}}{d x ^{2}} (x e^{- \frac{x ^{2}}{2}})

e^{- \frac{x ^{2}}{2}} x^{3} - 3 e^{- \frac{x ^{2}}{2}} x

Solution steps

\frac{d ^{2}}{d x ^{2}} (x e^{- \frac{x ^{2}}{2}})

\frac{d}{d x} (x e^{- \frac{x ^{2}}{2}}) = e^{- \frac{x ^{2}}{2}} - e^{- \frac{x ^{2}}{2}} x^{2}

= \frac{d}{d x} (e^{- \frac{x ^{2}}{2}} - e^{- \frac{x ^{2}}{2}} x^{2})

\frac{d}{d x} (e^{- \frac{x ^{2}}{2}} - e^{- \frac{x ^{2}}{2}} x^{2}) = e^{- \frac{x ^{2}}{2}} x^{3} - 3 e^{- \frac{x ^{2}}{2}} x

= e^{- \frac{x ^{2}}{2}} x^{3} - 3 e^{- \frac{x ^{2}}{2}} x

What is (d^2}{dx^2}(xe^{-\frac{x^2)/2}) ?
The answer to (d^2}{dx^2}(xe^{-\frac{x^2)/2}) is e^{-(x^2)/2}x^3-3e^{-(x^2)/2}x