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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- 2 x^{3} + 2) = - 6 x^{2}

= e^{- 2 x^{3} + 2} (- 6 x^{2})

Simplify

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

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