There is something I don't understand about the recent concept of a "number derivative". It seems to me that the (very illusorious) 'relation' to the real derivative is driving the interest, while a more general pursuit should be in place.(adsbygoogle = window.adsbygoogle || []).push({});

I mean,anyfunction satisfying the Leibniz rule, f(ab) = a f(b) + b f(a) will comply with the following,

[tex]

\begin{array}{ll}

\bullet & f(a^n) = n a^{n-1} f(a) \\

\bullet & f(n) = n \sum_{i=1}^k e_i \frac{f(p_i)}{p_i} \,, \quad

\mbox{where } n = p_1^{e_1} p_2^{e_2} ... p_k^{e_k}

[/tex]

without any need of defining f(p) = 1 for p prime, which is just a particular case.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Number derivative

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**