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Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

= \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

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x \to 0 lim (\frac{1}{x - x ^{2}} - \frac{1}{x})

Frequently Asked Questions (FAQ)

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