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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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f (x) = \frac{( e ^{x} )}{x ^{2} + 1}

x \to 3 lim (\frac{5 x}{6 - 2 x})

\int \frac{( x ^{2} )}{9 - x ^{2}} d x

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