Question

How do you find the derivative of `ln(ln x)`?

Answer 1

Using chain rule and, after that, logarithm's derivation rule.

In order to use the chain rule, let's consider your function `ln(u)`, where evidently `u` stands for `lnx`.

Derivating `ln(u)`, we get `(u')/u`, where `u'` is the derivative of our `u`, which we have already stated is `lnx`.

Proceeding, `(dln(lnx))/(dx) = ((1/x)/lnx) = 1/(x*lnx)`.