Find the Derivative minus d divide dx one divide(x to the power of five)

$\frac{1}{x^{5}}$

Apply basic rules of exponents.

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Rewrite $\frac{1}{x^{5}}$ as ${(x^{5})}^{- 1}$ .

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

Multiply the exponents in ${(x^{5})}^{- 1}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{d}{d x} [x^{5 \cdot - 1}]$

Multiply $5$ by $- 1$ .

$\frac{d}{d x} [x^{- 5}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 5$ .

$- 5 x^{- 6}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Combine terms.

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Combine $- 5$ and $\frac{1}{x^{6}}$ .

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

Move the negative in front of the fraction.

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

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