# How do you find d/dx ln(ln(x))?

Using the Chain Rule you first derive the "outside" $\ln$ leaving the argumet (the other $\ln$) as it is and then multiply times the derivative of the internal $\ln$ (the argument of the first).
$\frac{d}{\mathrm{dx}} \ln \left(\ln \left(x\right)\right) = \frac{1}{\ln} \left(x\right) \cdot \frac{1}{x} = \frac{1}{x \ln \left(x\right)}$