What is the derivative of x^{-1/5} ?

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

What is the first derivative of x^{-1/5} ?

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

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\frac{d}{d x} (x^{- \frac{1}{5}})

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

Solution steps

\frac{d}{d x} (x^{- \frac{1}{5}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{1}{5} x^{- \frac{1}{5} - 1}

Simplify

- \frac{1}{5} x^{- \frac{1}{5} - 1} : - \frac{1}{5 x ^{\frac{6}{5}}}

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

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f (x) = (x + 1) (x + 1 - \frac{1}{x + 2})

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