# the word “derivative”

When did the word "derivative" come into use in calculus, and why?

As in Can the word "derive" be used to mean "take the derivative of"? the word "derivative" in normal English means "stemming from". But $\int f$ "derives" from $f$ just as much as does $f'$, and $f'$ "integrates" information from $f$ just as much as does $f'$. So who decided that a ratio of fluxions should be called the derivative, and why?

• You mean to ask what the derivative of "derivative" is? – fretty Jan 6 '14 at 18:10
• @fretty Haha. Yes. From where did "derivative" derive? – isomorphismes Jan 7 '14 at 0:31

• @MPW I agree that "differentiate" captures the sense of $f(x-h)-f(x)$ much better—it sounds almost like "difference", which is good. But then the question arises, why use "derivative" for the infinitesimal version instead of just "differences" (or "self-differences")? As en.wikipedia.org/wiki/History_of_calculus notes, at some point we started dropping "infinitesimal" from "the infinitesimal calculus"—a disservice to all the other creative people who invented other interesting calculi! – isomorphismes Jan 7 '14 at 0:28
• Leibniz used the term "differential" to emphasize the transition from finite differences to infinitesimal differences. His $dx$ and $dy$ and their properties were definitely inspired by finite differences and their properties, but they were not the same thing. That's why he introduced a new term. As far as calculus is concerned, what is dropped is not merely the word "infinitesimal" but infinitesimals themselves, as you may find out to your chagrin if you go to college. This was supposed to be a humorous remark :-) – Mikhail Katz Jan 7 '14 at 13:47