Based on the geometry of the three difference quotients in calculus, it seems there should be a general form $$P(f(x + h) - f(x)) + (1 - P)(f(x) - f(x - h))\over h$$ where $0 <= P <= 1$, at least if $P$ is real.
Is there a name for this form, or any utility for it? Can $P$ ever be a non-real complex number?