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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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