# Number derivative

1. Nov 21, 2009

### dodo

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.

I mean, any function satisfying the Leibniz rule, f(ab) = a f(b) + b f(a) will comply with the following,
$$\begin{array}{ll} \bullet & f(a^n) = n a^{n-1} f(a) \\ \bullet & f(n) = n \sum_{i=1}^k e_i \frac{f(p_i)}{p_i} \,, \quad \mbox{where } n = p_1^{e_1} p_2^{e_2} ... p_k^{e_k}$$
without any need of defining f(p) = 1 for p prime, which is just a particular case.