# What is the derivative of f(x)=ln(ln(x))?

$\frac{1}{x \ln \left(x\right)}$
According to the chain rule, $\frac{d}{\mathrm{dx}} \left[\ln \left(u\right)\right] = u ' \cdot \frac{1}{u}$, and we have $u = \ln \left(x\right)$, hence
$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[\ln \left(x\right)\right] \cdot \frac{1}{\ln \left(x\right)} = \frac{1}{x} \cdot \frac{1}{\ln \left(x\right)} = \frac{1}{x \ln \left(x\right)}$