Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises - Page 211: 14

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

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