What is the derivative of f(x)=x^{-8} ?

The derivative of f(x)=x^{-8} is -8/(x^9)

What is the first derivative of f(x)=x^{-8} ?

The first derivative of f(x)=x^{-8} is -8/(x^9)

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derivative of

f (x) = x^{- 8}

- \frac{8}{x ^{9}}

Solution steps

\frac{d}{d x} (x^{- 8})

Apply the Power Rule:

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

= - 8 x^{- 8 - 1}

Simplify

- 8 x^{- 8 - 1} : - \frac{8}{x ^{9}}

= - \frac{8}{x ^{9}}

What is the derivative of f(x)=x^{-8} ?
The derivative of f(x)=x^{-8} is -8/(x^9)
What is the first derivative of f(x)=x^{-8} ?
The first derivative of f(x)=x^{-8} is -8/(x^9)