Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - Chapter 6 Review Exercises - Page 485: 22

$$y' = \frac{{2\ln x}}{x}$$

$$\eqalign{ & y = {\left( {\ln x} \right)^2} \cr & {\text{find the derivative}} \cr & y' = \left( {{{\left( {\ln x} \right)}^2}} \right)' \cr & {\text{use chain rule}} \cr & y' = 2\left( {\ln x} \right)\left( {\ln x} \right)' \cr & {\text{use }}\left( {\ln u} \right)' = \frac{{u'}}{u}, \cr & y' = 2\left( {\ln x} \right)\left( {\frac{1}{x}} \right) \cr & {\text{simplifying}} \cr & y' = \frac{{2\ln x}}{x} \cr} $$