#### Answer

$$\frac{1}{{x\ln x}}$$

#### Work Step by Step

$$\eqalign{
& \frac{d}{{dx}}\left( {\ln \left( {\ln x} \right)} \right) \cr
& {\text{use the rule }}\frac{d}{{dx}}\left( {\ln u} \right) = \frac{1}{u}\frac{{du}}{{dx}},{\text{ letting }}u = \ln x \cr
& = \frac{1}{{\ln x}}\frac{d}{{dx}}\left( {\ln x} \right) \cr
& = \frac{1}{{\ln x}}\left( {\frac{1}{x}} \right) \cr
& {\text{multiply}} \cr
& = \frac{1}{{x\ln x}} \cr} $$