Note that the extra revenue from an incremental unit of quantity, Δ(PQ)/ΔQ, has two components:
1. Producing one extra unit and selling it at price P brings in revenue (1)(P) = P.
2. But because the firm faces a downward-sloping demand curve, producing and selling this extra unit also results in a small drop in price ΔP/ΔQ, which reduces the revenue from all units sold (i.e., a change in revenue Q[ΔP/ΔQ]).
Thus,