Question

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

Answer 1

`1/ (x ln(x) )`

Explanation:

chain rule

`y = ln(ln(x))`

`dy/dx = 1/(lnx) d/dx (lnx)= 1/(lnx) 1/x = 1/ (x ln(x) )`

in detail

let `y = ln p` and `p = ln x`
`dy/(dp) = 1/p`

`(dp)/dx = 1/x`

`dy/dx = dy/(dp) * (dp)/dx = 1/p * 1/x = 1/ (x ln(x) )`