# Calculate the derivatives of the functions. f(x)=(4x-1)^{-1}f(x)=(x+7)^{-2}

Calculate the derivatives of the functions.
$f\left(x\right)={\left(4x-1\right)}^{-1}f\left(x\right)={\left(x+7\right)}^{-2}$
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$f\left(x\right)={\left(x+7\right)}^{-2}$
Differentiate both sides with respect to x
${f}^{\prime }\left(x\right)=\frac{d}{dx}\left[{\left(x+7\right)}^{-2}\right]$
Apply The Generalized Power Rule $\frac{d}{dx}\left[{u}^{n}\right]={\nu }^{n-1}\frac{du}{dx}$, let u=x+7
${f}^{\prime }\left(x\right)=-2{\left(x+7\right)}^{-2-1}\frac{d}{dx}\left[x+7\right]$
Therefore,
${f}^{\prime }\left(x\right)=-2{\left(x+7\right)}^{-3}\left(1\right)$
Simplify
${f}^{\prime }\left(x\right)=-{\frac{2}{x+7}}^{3}$