What is (\partial)/(\partial x)(e^{-ax^2}) ?

The answer to (\partial)/(\partial x)(e^{-ax^2}) is -2ae^{-ax^2}x

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(\partial)/(\partial x)(e^{-ax^2})

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

(x + 4)^{2} y^{^{'}} + 3 (x + 4) y = 4

\int \frac{50}{( x - 1 ) ( x ^{2} + 49 )} d x

ln (e^{x^{2}})

\int \frac{x ^{2}}{x ^{2} - 4 x + 13} d x

\int \frac{e ^{4 x}}{2} d x

What is (\partial)/(\partial x)(e^{-ax^2}) ?
The answer to (\partial)/(\partial x)(e^{-ax^2}) is -2ae^{-ax^2}x