Question

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power rule (with rewriting the expression)
$\frac{d}{dx}(\frac{1}{x^{9}})=$

Explanation:

Step1: Rewrite the function

Rewrite $\frac{1}{x^{9}}$ as $x^{- 9}$ using the rule $\frac{1}{a^{n}}=a^{-n}$.

Step2: Apply power - rule for differentiation

The power - rule for differentiation is $\frac{d}{dx}(x^{n})=nx^{n - 1}$. For $y = x^{-9}$, we have $n=-9$. Then $\frac{d}{dx}(x^{-9})=-9x^{-9 - 1}=-9x^{-10}$.

Answer:

$- \frac{9}{x^{10}}$