differentiable (idea)

A function f:D->R is said to be differentiable at a point t in D if the quotient function q defined by:
q(h) = (f(t+h)-f(t))/h
converges at 0. That is, for some real number L,
for all e > 0 and all s in (-t)+D, i.e. {t-x | for all x in D}, 0 < |s| < d(e) implies |q(s)-L| < e.
L is then called the derivative of f at t.

If f is differentiable at every point of D, f is said to be differentiable on D.