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Popular >

derivative of e^{-1/2 x^2}

Solution

\frac{d}{d x} (e^{- \frac{1}{2} x^{2}})

Solution

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

Solution steps

\frac{d}{d x} (e^{- \frac{1}{2} x^{2}})

Simplify

e^{- \frac{1}{2} x^{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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derivative of f(x)=(5+x^4)^{3x}derivative of

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(\partial)/(\partial y)(x^3+ky^2-5xy)

\frac{\partial}{\partial y} (x^{3} + k y^{2} - 5 x y)

derivative of (x^2-7^2)

\frac{d}{d x} ((x^{2} - 7)^{2})

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y = - \frac{8 x}{x ^{2} + 1}

Frequently Asked Questions (FAQ)

What is the derivative of e^{-1/2 x^2} ?
The derivative of e^{-1/2 x^2} is -e^{-(x^2)/2}x
What is the first derivative of e^{-1/2 x^2} ?
The first derivative of e^{-1/2 x^2} is -e^{-(x^2)/2}x