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

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

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

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

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

- 2 e^{- x^{2}} x

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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\frac{1}{2 π} e^{- \frac{0. 4 ^{2}}{2}}

x y^{2} z^{2}