#### Answer

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

#### Work Step by Step

Using Quotient Rule and Chain Rule
$\frac{d}{dx}\left(\frac{ln(x^2)}{x}\right) = \frac{\left(\frac{2x}{x^2}\right)(x)-(ln(x^2))(1)}{x^2} = \frac{2-ln(x^2)}{x^2}$