The standard derivative, for example $\frac{d}{dx}x^2 = 2x, $ gives the slope of a function at a particular point. Does the arithmetic derivative have a similarly simple geometric interpretation?
As a specific example, how might I show graphically that $1'=0$, that $2'=1$ or that $8'=12$?
EDIT: The arithmetic derivative can be defined as follows:
$p'=1$ for any prime, $p$
$(pq)'= p'q + pq'$ for any $p,q \in \mathbb{N}$
(Source: Wikipedia)
From the above, rules analogous to the power and quotient rules can be derived.
For a frenetic introduction, please see this YouTube video.