What is the derivative of e^{-x^7} ?

The derivative of e^{-x^7} is -7e^{-x^7}x^6

What is the first derivative of e^{-x^7} ?

The first derivative of e^{-x^7} is -7e^{-x^7}x^6

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\frac{d}{d x} (e^{- x^{7}})

- 7 e^{- x^{7}} x^{6}

Solution steps

\frac{d}{d x} (e^{- x^{7}})

Apply the chain rule:

e^{- x^{7}} \frac{d}{d x} (- x^{7})

= e^{- x^{7}} \frac{d}{d x} (- x^{7})

\frac{d}{d x} (- x^{7}) = - 7 x^{6}

= e^{- x^{7}} (- 7 x^{6})

Simplify

= - 7 e^{- x^{7}} x^{6}

What is the derivative of e^{-x^7} ?
The derivative of e^{-x^7} is -7e^{-x^7}x^6
What is the first derivative of e^{-x^7} ?
The first derivative of e^{-x^7} is -7e^{-x^7}x^6