Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 25

$$y' = \frac{{2\cot x}}{{\ln 10}}$$

$$\eqalign{ & y = \log \left( {{{\sin }^2}x} \right) \cr & {\text{differentiate}} \cr & y' = \frac{{\left( {{{\sin }^2}x} \right)'}}{{\left( {\ln 10} \right){{\sin }^2}x}} \cr & {\text{chain rule }} \cr & y' = \frac{{2\sin x\left( {\cos x} \right)}}{{\left( {\ln 10} \right){{\sin }^2}x}} \cr & {\text{simplify}} \cr & y' = \frac{{2\left( {\cos x} \right)}}{{\left( {\ln 10} \right)\sin x}} \cr & y' = \frac{{2\cot x}}{{\ln 10}} \cr} $$