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

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

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

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

- 2 k e^{- k x^{2}} x

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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