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

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Answer 1 · 2015-05-13T17:41:19

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

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

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

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

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