Difference quotient

The Difference quotient is used in Calculus to compute the slope of a secant line through two points on a graph of a function f(x).

<math>\frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math>

How the Difference quotient differs from the Derivative

The difference between the difference quotient and the derivative is that the derivative is the value of the difference quotient as the secant lines get closer and closer to the tangent line:

<math>f'(x)=\lim _{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\,\!</math>