What is the derivative of e^{-6x^5} ?

The derivative of e^{-6x^5} is -30e^{-6x^5}x^4

What is the first derivative of e^{-6x^5} ?

The first derivative of e^{-6x^5} is -30e^{-6x^5}x^4

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\frac{d}{d x} (e^{- 6 x^{5}})

- 30 e^{- 6 x^{5}} x^{4}

Solution steps

\frac{d}{d x} (e^{- 6 x^{5}})

Apply the chain rule:

e^{- 6 x^{5}} \frac{d}{d x} (- 6 x^{5})

= e^{- 6 x^{5}} \frac{d}{d x} (- 6 x^{5})

\frac{d}{d x} (- 6 x^{5}) = - 30 x^{4}

= e^{- 6 x^{5}} (- 30 x^{4})

Simplify

= - 30 e^{- 6 x^{5}} x^{4}

f (x) = x^{2} - 7

\int \frac{5}{( x + 1 ) ( x ^{2} + 4 )} d x

\int t^{2} 1 + t^{2} d t

\frac{d}{d x} (- x^{2} + 9)

\frac{7 e ^{x}}{( 7 + e ^{x} ) ^{2}}

What is the derivative of e^{-6x^5} ?
The derivative of e^{-6x^5} is -30e^{-6x^5}x^4
What is the first derivative of e^{-6x^5} ?
The first derivative of e^{-6x^5} is -30e^{-6x^5}x^4