When I was learning about why marginal revenue is lower than demand, I referred to this derivation:
$$\frac{d(TR)}{dQ} = \frac{d(PQ)}{dQ} = \frac{PdQ + QdP}{dQ} = P + Q\frac{dP}{dQ}$$
Wikipedia explains that marginal revenue is the "change in revenue for some change in quantity sold, to that change in quantity sold" (https://en.wikipedia.org/wiki/Marginal_revenue) and uses TR in the derivation, as in total revenue.
However, this is confusing for me, because the function that describes the total revenue over the history of the firm is not equal to the function used above, PQ. Is marginal revenue instead the change in daily revenue for its corresponding change in daily quantity sold? (Or maybe hourly, or weekly, depending on the rate at which that good is actually sold?)
This makes more sense to me, since total revenue is an accumulation over time of the daily marginal revenue.