The difference quotient (f(x+h) − f(x))/h is the average rate of change over a small interval. The derivative is its limit as h → 0.
Derivative
f'(x) = lim(h→0) (f(x+h) − f(x))/h
The difference quotient (f(x+h) − f(x))/h is the average rate of change over a small interval. The derivative is its limit as h → 0.