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}

Popular >

(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}}

y = 7 x - 6 x, (1, 1)

y^{^{''}} + 9 y^{^{'}} - 10 y = 0

\frac{d y}{d x} = 2 + y - 2 x + 3

\int \frac{x ^{3}}{( x ^{2} + 16 ) ^{3}} d x

\int \frac{2 x + 7}{x ^{2} + 2 x + 5} d x

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}