Answer
$$y' = \frac{1}{{\ln x\ln 10}}$$
Work Step by Step
$$\eqalign{
& y = \log \left( {\ln x} \right) \cr
& {\text{find the derivative}} \cr
& y' = \left( {\log \left( {\ln x} \right)} \right)' \cr
& {\text{use }}\left( {{{\log }_a}u} \right)' = \frac{{u'}}{{u\ln a}} \cr
& y' = \frac{{\left( {\ln x} \right)'}}{{\left( {\ln x} \right)\ln 10}} \cr
& {\text{compute derivative}} \cr
& y' = \frac{{\left( {1/x} \right)}}{{\left( {\ln x} \right)\ln 10}} \cr
& {\text{simplifying}} \cr
& y' = \frac{1}{{\ln x\ln 10}} \cr} $$
