Question

What is the derivative of `ln(ln(lnx))`?

Answer 1

We'll use chain rule here, which states that `(dy)/(dx)=(dy)/(du)(du)/(dv)(dv)/(dx)`

Explanation:

Renaming:

`f(x)=ln(u)`
`u=ln(v)`
`v=ln(x)`

We can now proceed.

`(dy)/(dx)=1/u1/v1/x=1/(uvx)=1/(ln(v)vx)=color(green)(1/(ln(ln(x))(ln(x))x))`