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

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

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

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

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

Solution steps

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

Simplify

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

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

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

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

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

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

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