Thomas' Calculus 13th Edition

$$\frac{3}{x}$$
\eqalign{ & y = \ln {x^3} \cr & {\text{use the property of logarithms }}\ln {a^n} = n\ln a \cr & y = 3\ln x \cr & {\text{Find the derivative of }}y{\text{ with respect to }}x \cr & \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {3\ln x} \right] \cr & {\text{Apply the constant multiple rule}} \cr & \frac{{dy}}{{dx}} = 3\frac{d}{{dx}}\left[ {\ln x} \right] \cr & {\text{use the formula }}\cr & \frac{d}{{dx}}\ln u = \frac{1}{u}\frac{{du}}{{dx}}{\text{, }}u > 0\cr & {\text{ where }}u{\text{ is any differentiable function of }}x \cr & {\text{then:}} \cr & \frac{{dy}}{{dx}} = 3\left( {\frac{1}{x}} \right) \cr & {\text{solve the derivative and simplify}} \cr & \frac{{dy}}{{dx}} = \frac{3}{x} \cr}