What is the derivative of 1/(e^{x^2}) ?

The derivative of 1/(e^{x^2}) is -2e^{-x^2}x

What is the first derivative of 1/(e^{x^2}) ?

The first derivative of 1/(e^{x^2}) is -2e^{-x^2}x

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\frac{d}{d x} (\frac{1}{e ^{x^{2}}})

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

Solution steps

\frac{d}{d x} (\frac{1}{e ^{x^{2}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the derivative of 1/(e^{x^2}) ?
The derivative of 1/(e^{x^2}) is -2e^{-x^2}x
What is the first derivative of 1/(e^{x^2}) ?
The first derivative of 1/(e^{x^2}) is -2e^{-x^2}x