# What is the derivative of ln(ln(2x))?

The answer is: $y ' = \frac{1}{x \ln x}$
$y = f \left(g \left(x\right)\right) \Rightarrow y ' = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$.
$y ' = \frac{1}{\ln} \left(2 x\right) \cdot \frac{1}{2 x} \cdot 2 = \frac{1}{x \ln x}$.