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

The derivative of e^{-kx^2} is -2ke^{-kx^2}x

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

The first derivative of e^{-kx^2} is -2ke^{-kx^2}x

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int_{1}^{\infty} \frac{1}{3 x - 2} d x

\int \frac{2 x + 1}{x ^{2} + 5 x + 6} d x

\frac{d}{d x} (2 x^{2} + 5)

\int 4 x^{2} e^{3 x} d x

y^{^{''}} + y = 3 e^{- 4 x}

What is the derivative of e^{-kx^2} ?
The derivative of e^{-kx^2} is -2ke^{-kx^2}x
What is the first derivative of e^{-kx^2} ?
The first derivative of e^{-kx^2} is -2ke^{-kx^2}x