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\newcommand\ds{\displaystyle}

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QUESTION

Differentiate the function $\ds\frac{\ln x}{x^2}$ with respect to
$x$.

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ANSWER

$\ds\frac{d}{dx}\left(\frac{\ln
x}{x^2}\right)=\frac{x^2\left(\frac{1}{x}\right)-(\ln
x)(2x)}{(x^2)^2}=\frac{x-2x\ln x}{x^4}=\frac{1-2\ln x}{x^3}$




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