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}

\int (x^{2} + 3) sin (x) d x

y = 3 (1)^{2} - 5 (1) + 9

\int \frac{cos ( x )}{sin ^{4} ( x ) - 16} d x

\int \frac{2 x ^{2} - 4}{x ^{2} ( x - 2 )} d x

y = x (x - 14)

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