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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

n = 0 \sum \infty \frac{e ^{n}}{π ^{n}}

\frac{d}{d x} (3 (4 e^{2 x} x + 4 e^{2 x}))

\int \frac{x}{10 - x ^{2}} d x

n = 1 \sum \infty \frac{1}{( 2 n - 1 )}

\int 7 sin^{4} (x) cos^{2} (x) d x

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