The Derivative as a Rate of Measure

A Business Reading of "Rate of Measure"

If $C(x)$ is the total cost of producing $x$ units, its derivative $\dfrac{dC}{dx}$ is the marginal cost — the (instantaneous) rate at which total cost rises as output rises, which in practice is read as "the approximate extra cost of producing one more unit near the current output level." The same idea gives marginal revenue ($\dfrac{dR}{dx}$, from a revenue function $R(x)$) and marginal profit ($\dfrac{d\Pi}{dx}$, from a profit function $\Pi(x)$). This rate-of-change reading — not a re-derivation from the limit definition — is exactly how this chapter uses the derivative in §9's applications. …