[Chinjut]

It seems to me a sum should be at least as large as each of its summands (or rather, it once did). The world paid no heed, and life trudged on. I don't see a need to pick one particular archetypal trait or another and say the word "derivative" (or any other bit of mathematical jargon) mustn't ever be extended by analogy to a situation no longer directly manifesting that trait. A web of family resemblances doesn't depend on any one fiber running through all of it.

It's not as though the similarity of terminology is chosen with intent to confuse; the intent is to illuminate. The name for the generalization is chosen to match its more familiar relative because it is often _useful_ to think in terms of the analogy, imperfect though it be. [It seems humans are such that we would never find our way to powerful abstractions without such overloading; the combinatorial explosion of names would be too great to comprehend.]