Chapter 3 - Section 3.8 - Derivatives of Inverse Functions and Logarithms - Exercises - Page 175: 19

$$y'=\frac{3}{x}$$

$$y=\ln(x^3)$$ Recall the following Derivative Rules: $$\frac{d}{dx}(\ln u)=\frac{1}{u}\frac{du}{dx}$$ Therefore, we have $$y'=\Big(\ln(x^3)\Big)'=\frac{1}{x^3}\times(x^3)'=\frac{3x^2}{x^3}$$ $$y'=\frac{3}{x}$$