# Math Help - fractional derivative (order t) of (log x)^n (n a positive integer)?

1. ## fractional derivative (order t) of (log x)^n (n a positive integer)?

Hi, I'd be grateful if someone could tell me the fractional derivative (order t, where t is not necessarily an integer) of the following functions:

1) ln x, (ln x)^2, (ln x)^3, and more generally, (ln x)^n where n is a positive integer, and

2) ln(ln x), ln(ln(ln x)), and more generally, ln(...(ln x)...), with n nested ln functions, where n is a positive integer.

Most important to me are the fractional derivatives of (ln x)^n and ln(ln x).

Many thanks! Michael

2. This would be an excellent exploration of the fundamental definition of a derivative. Let's see what you get.