What is the derivative of-9e^{x^{-9}} ?

The derivative of-9e^{x^{-9}} is (81e^{1/(x^9)})/(x^{10)}

What is the first derivative of-9e^{x^{-9}} ?

The first derivative of-9e^{x^{-9}} is (81e^{1/(x^9)})/(x^{10)}

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derivative of

- 9 e^{x^{- 9}}

\frac{81 e ^{\frac{1}{x ^{9}}}}{x ^{10}}

Solution steps

\frac{d}{d x} (- 9 e^{x^{- 9}})

Take the constant out:

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

= - 9 \frac{d}{d x} (e^{x^{- 9}})

Apply the chain rule:

e^{x^{- 9}} \frac{d}{d x} (x^{- 9})

= e^{x^{- 9}} \frac{d}{d x} (x^{- 9})

\frac{d}{d x} (x^{- 9}) = - \frac{9}{x ^{10}}

= - 9 e^{x^{- 9}} (- \frac{9}{x ^{10}})

Simplify

- 9 e^{x^{- 9}} (- \frac{9}{x ^{10}}) : \frac{81 e ^{\frac{1}{x ^{9}}}}{x ^{10}}

= \frac{81 e ^{\frac{1}{x ^{9}}}}{x ^{10}}

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What is the derivative of-9e^{x^{-9}} ?
The derivative of-9e^{x^{-9}} is (81e^{1/(x^9)})/(x^{10)}
What is the first derivative of-9e^{x^{-9}} ?
The first derivative of-9e^{x^{-9}} is (81e^{1/(x^9)})/(x^{10)}