What is the derivative of e^{-(x^2/2}) ?

The derivative of e^{-(x^2/2}) is -e^{-(x^2)/2}x

What is the first derivative of e^{-(x^2/2}) ?

The first derivative of e^{-(x^2/2}) is -e^{-(x^2)/2}x

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{1}{3 x ^{3}} d x

\int (\frac{d}{1} (x)) d x

y = x 2^{x}

y^{^{''}} + 25 y = cos (5 x)

\frac{d}{d x} ((x - 2) (x^{2} + 4))

What is the derivative of e^{-(x^2/2}) ?
The derivative of e^{-(x^2/2}) is -e^{-(x^2)/2}x
What is the first derivative of e^{-(x^2/2}) ?
The first derivative of e^{-(x^2/2}) is -e^{-(x^2)/2}x