In single-variable calculus, the difference quotient is usually the name for the expression {\frac {f-f(x)}{h}} which when taken to the limit as h approaches 0 gives the derivative of the function f.

What do you mean by difference quotient?

The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change.

Why do you use difference quotient?

The difference quotient allows us to compute the slope of secant lines. A secant line is nearly the same as a tangent line, but it instead goes through at least two points on a function. Finally, with some cancelling of terms, we can arrive at the very definition of the difference quotient.