Answer
$$\frac{{3{{\left( {\ln x} \right)}^2}}}{x}$$
Work Step by Step
$$\eqalign{
& y = {\left( {\ln x} \right)^3} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{{\left( {\ln x} \right)}^3}} \right] \cr
& {\text{use the general power rule for derivatives }}\cr
& \frac{d}{{dx}}\left[ {{u^n}} \right] = n{u^{n - 1}}\frac{{du}}{{dx}} \cr
& \frac{{dy}}{{dx}} = 3{\left( {\ln x} \right)^{3 - 1}}\frac{d}{{dx}}\left[ {\ln x} \right] \cr
& {\text{solve the derivative and simplify}} \cr
& \frac{{dy}}{{dx}} = 3{\left( {\ln x} \right)^2}\left( {\frac{1}{x}} \right) \cr
& \frac{{dy}}{{dx}} = \frac{{3{{\left( {\ln x} \right)}^2}}}{x} \cr} $$
