Answer
$-\frac{1}{x}$
Work Step by Step
$\frac{d}{dx}\ln\frac{1}{x}$
$=\frac{1}{\frac{1}{x}}\frac{d}{dx}\frac{1}{x}$
$=x*-x^{-2}$
$=-x^{-1}$
$=-\frac{1}{x}$
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