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

The derivative of e^{-bx^2} is -2be^{-bx^2}x

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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