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

The derivative of e^{-5x^4} is -20e^{-5x^4}x^3

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

The first derivative of e^{-5x^4} is -20e^{-5x^4}x^3

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

- 20 e^{- 5 x^{4}} x^{3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- 5 x^{4}) = - 20 x^{3}

= e^{- 5 x^{4}} (- 20 x^{3})

Simplify

= - 20 e^{- 5 x^{4}} x^{3}

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What is the derivative of e^{-5x^4} ?
The derivative of e^{-5x^4} is -20e^{-5x^4}x^3
What is the first derivative of e^{-5x^4} ?
The first derivative of e^{-5x^4} is -20e^{-5x^4}x^3