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

The derivative of 4e^{-x^4} is -16e^{-x^4}x^3

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

The first derivative of 4e^{-x^4} is -16e^{-x^4}x^3

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

- 16 e^{- x^{4}} x^{3}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= - 16 e^{- x^{4}} x^{3}

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What is the derivative of 4e^{-x^4} ?
The derivative of 4e^{-x^4} is -16e^{-x^4}x^3
What is the first derivative of 4e^{-x^4} ?
The first derivative of 4e^{-x^4} is -16e^{-x^4}x^3