What is the derivative of ae^{-b^2x^2} ?

The derivative of ae^{-b^2x^2} is -2ab^2e^{-b^2x^2}x

What is the first derivative of ae^{-b^2x^2} ?

The first derivative of ae^{-b^2x^2} is -2ab^2e^{-b^2x^2}x

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the derivative of ae^{-b^2x^2} ?
The derivative of ae^{-b^2x^2} is -2ab^2e^{-b^2x^2}x
What is the first derivative of ae^{-b^2x^2} ?
The first derivative of ae^{-b^2x^2} is -2ab^2e^{-b^2x^2}x