What is the derivative of (ln(x))^x?

1 Answer
Dec 24, 2015

We can go by using chain rule and also the rule to derivate exponential functions.

Explanation:

Chain rule states that (dy)/(dx)=(dy)/(du)(du)/(dx).
We'll also need the rule to derivate exponential functions, which is: be f(x)=a^u, then f'(x)=a^u(lna)u'

Let's rename u=lnx.

Solving:

(dy)/(dx)=(lnx)^(x)(ln(lnx))*1