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

The derivative of 6e^{x^{-5}} is -(30e^{1/(x^5)})/(x^6)

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

The first derivative of 6e^{x^{-5}} is -(30e^{1/(x^5)})/(x^6)

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derivative of

6 e^{x^{- 5}}

- \frac{30 e ^{\frac{1}{x ^{5}}}}{x ^{6}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

6 e^{x^{- 5}} (- \frac{5}{x ^{6}}) : - \frac{30 e ^{\frac{1}{x ^{5}}}}{x ^{6}}

= - \frac{30 e ^{\frac{1}{x ^{5}}}}{x ^{6}}

f (x) = \frac{1}{3 + 2 x}, (1, \frac{1}{5})

\frac{d}{d x} (\frac{c x + b}{4 x + d})

\frac{d ^{2}}{d x ^{2}} (cos (x^{2}))

\int - x^{5} sin (x) d x

x \to 0 lim (500)

What is the derivative of 6e^{x^{-5}} ?
The derivative of 6e^{x^{-5}} is -(30e^{1/(x^5)})/(x^6)
What is the first derivative of 6e^{x^{-5}} ?
The first derivative of 6e^{x^{-5}} is -(30e^{1/(x^5)})/(x^6)