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

  1. #1
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    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
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  2. #2
    MHF Contributor
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    This would be an excellent exploration of the fundamental definition of a derivative. Let's see what you get.
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