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Popular Calculus >

derivative of 1/(5x^8)

Solution

\frac{d}{d x} (\frac{1}{5 x ^{8}})

Solution

- \frac{8}{5 x ^{9}}

Solution steps

\frac{d}{d x} (\frac{1}{5 x ^{8}})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{1}{x ^{8}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{1}{5} \frac{d}{d x} (x^{- 8})

Apply the Power Rule:

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

= \frac{1}{5} (- 8 x^{- 8 - 1})

Simplify

\frac{1}{5} (- 8 x^{- 8 - 1}) : - \frac{8}{5 x ^{9}}

= - \frac{8}{5 x ^{9}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(5x^8) ?
The derivative of 1/(5x^8) is -8/(5x^9)
What is the first derivative of 1/(5x^8) ?
The first derivative of 1/(5x^8) is -8/(5x^9)