What is the derivative of e^{-x^5} ?

The derivative of e^{-x^5} is -5e^{-x^5}x^4

What is the first derivative of e^{-x^5} ?

The first derivative of e^{-x^5} is -5e^{-x^5}x^4

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derivative of

e^{- x^{5}}

- 5 e^{- x^{5}} x^{4}

Solution steps

\frac{d}{d x} (e^{- x^{5}})

Apply the chain rule:

e^{- x^{5}} \frac{d}{d x} (- x^{5})

= e^{- x^{5}} \frac{d}{d x} (- x^{5})

\frac{d}{d x} (- x^{5}) = - 5 x^{4}

= e^{- x^{5}} (- 5 x^{4})

Simplify

= - 5 e^{- x^{5}} x^{4}

What is the derivative of e^{-x^5} ?
The derivative of e^{-x^5} is -5e^{-x^5}x^4
What is the first derivative of e^{-x^5} ?
The first derivative of e^{-x^5} is -5e^{-x^5}x^4