As an economic application of the quotient rule, let us consider the rate of change of average cost when output varies.
Given a total-cost function C = C[Q], the average-cost [AC] function is a quotient of two functions of Q> since AC = C[Q]/Q, defined as long as Q > 0. Therefore, the rate of change of AC with respect to Q can be found by differentiating AC:
From this it follows that, for Q > 0, d C[Q]> dQ Q