What is the derivative of e^{-6x^2} ?

The derivative of e^{-6x^2} is -12e^{-6x^2}x

What is the first derivative of e^{-6x^2} ?

The first derivative of e^{-6x^2} is -12e^{-6x^2}x

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\frac{d}{d x} (e^{- 6 x^{2}})

- 12 e^{- 6 x^{2}} x

Solution steps

\frac{d}{d x} (e^{- 6 x^{2}})

Apply the chain rule:

e^{- 6 x^{2}} \frac{d}{d x} (- 6 x^{2})

= e^{- 6 x^{2}} \frac{d}{d x} (- 6 x^{2})

\frac{d}{d x} (- 6 x^{2}) = - 12 x

= e^{- 6 x^{2}} (- 12 x)

Simplify

= - 12 e^{- 6 x^{2}} x

What is the derivative of e^{-6x^2} ?
The derivative of e^{-6x^2} is -12e^{-6x^2}x
What is the first derivative of e^{-6x^2} ?
The first derivative of e^{-6x^2} is -12e^{-6x^2}x