Question

What is the derivative of `(lnx)^(3x)`?

Answer 1

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)^(3x)(ln(lnx))*3`