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

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

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

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

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

e^{x^{2}} \cdot 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}} \cdot 2 x

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