What is the derivative of f(x)=x^{-5} ?

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

What is the first derivative of f(x)=x^{-5} ?

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

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derivative of

f (x) = x^{- 5}

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

Solution steps

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

Apply the Power Rule:

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

= - 5 x^{- 5 - 1}

Simplify

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

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

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