# Using the Extended Power Rule Find the following derivatives. \frac{d}{dx}(\frac{9}{x^{5}})

Jaya Legge 2021-04-23 Answered
Using the Extended Power Rule Find the following derivatives.
$\frac{d}{dx}\left(\frac{9}{{x}^{5}}\right)$
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Step 1
$\frac{d}{dx}\left(\frac{9}{{x}^{5}}\right)=\frac{d}{dx}\left(9{x}^{-5}\right)$
Use the power rule of derivative which states
$\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}$
Thus
$\frac{d}{dx}\left(9{x}^{-5}\right)=9\left(-5\right){x}^{-6}$
$=-45{x}^{-6}$
$=\frac{-45}{{x}^{6}}$
Jeffrey Jordon