What is the derivative of e^{-x^8} ?

The derivative of e^{-x^8} is -8e^{-x^8}x^7

What is the first derivative of e^{-x^8} ?

The first derivative of e^{-x^8} is -8e^{-x^8}x^7

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\frac{d}{d x} (e^{- x^{8}})

- 8 e^{- x^{8}} x^{7}

Solution steps

\frac{d}{d x} (e^{- x^{8}})

Apply the chain rule:

e^{- x^{8}} \frac{d}{d x} (- x^{8})

= e^{- x^{8}} \frac{d}{d x} (- x^{8})

\frac{d}{d x} (- x^{8}) = - 8 x^{7}

= e^{- x^{8}} (- 8 x^{7})

Simplify

= - 8 e^{- x^{8}} x^{7}

What is the derivative of e^{-x^8} ?
The derivative of e^{-x^8} is -8e^{-x^8}x^7
What is the first derivative of e^{-x^8} ?
The first derivative of e^{-x^8} is -8e^{-x^8}x^7