Question

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

Answer 1

Using the chain rule.

Explanation:

You have to apply the chain rule that tells us

`\frac{d}{dx}f[g(x)]=f'[g(x)]g'(x)`.

The `f` here is the external `ln`, while the `g` is the internal `ln(x)`.
The derivative of the logarithm is

`\frac{d}{dx}ln(x)=1/x`

so the `f'[g(x)]=1/ln(x)`

and the `g'(x)=1/x`.
The final result is

`\frac{d}{dx}ln(ln(x))=1/ln(x)1/x=1/(xln(x))`.