What is the derivative of 2e^{-x^3} ?

The derivative of 2e^{-x^3} is -6e^{-x^3}x^2

What is the first derivative of 2e^{-x^3} ?

The first derivative of 2e^{-x^3} is -6e^{-x^3}x^2

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\frac{d}{d x} (2 e^{- x^{3}})

- 6 e^{- x^{3}} x^{2}

Solution steps

\frac{d}{d x} (2 e^{- x^{3}})

Take the constant out:

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

= 2 \frac{d}{d x} (e^{- x^{3}})

Apply the chain rule:

e^{- x^{3}} \frac{d}{d x} (- x^{3})

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

\frac{d}{d x} (- x^{3}) = - 3 x^{2}

= 2 e^{- x^{3}} (- 3 x^{2})

Simplify

= - 6 e^{- x^{3}} x^{2}

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What is the derivative of 2e^{-x^3} ?
The derivative of 2e^{-x^3} is -6e^{-x^3}x^2
What is the first derivative of 2e^{-x^3} ?
The first derivative of 2e^{-x^3} is -6e^{-x^3}x^2