What is the derivative of e^{-0.5x^2} ?

The derivative of e^{-0.5x^2} is -e^{-0.5x^2}x

What is the first derivative of e^{-0.5x^2} ?

The first derivative of e^{-0.5x^2} is -e^{-0.5x^2}x

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\frac{d}{d x} (e^{- 0.5 x^{2}})

- e^{- 0.5 x^{2}} x

Solution steps

\frac{d}{d x} (e^{- 0.5 x^{2}})

Apply the chain rule:

e^{- 0.5 x^{2}} \frac{d}{d x} (- 0.5 x^{2})

= e^{- 0.5 x^{2}} \frac{d}{d x} (- 0.5 x^{2})

\frac{d}{d x} (- 0.5 x^{2}) = - x

= e^{- 0.5 x^{2}} (- x)

Simplify

= - e^{- 0.5 x^{2}} x

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What is the derivative of e^{-0.5x^2} ?
The derivative of e^{-0.5x^2} is -e^{-0.5x^2}x
What is the first derivative of e^{-0.5x^2} ?
The first derivative of e^{-0.5x^2} is -e^{-0.5x^2}x