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Apologies if there is a duplicate somewhere; I couldn't find one.

The use of the root "deriv" in the context of differentiation seems odd: we have differentiation, differentials, differentiable, differential equations, and then for some odd reason, "derivative." Why/how did this happen?

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  • $\begingroup$ It's not correct, but I like to think of it also as the fact that if you see a displaced object you know it must've moved (via velocity), a speeding cars speed likely came from acceleration, and so on. Another hand wavey one, but if you think of functions as being defined by their properties (i.e. the patterns in the way they change) they're defined (or derived) from, it just seems to follow you'd call this a derivative. If it walks like a duck, and it quacks like a duck, it is a duck. $\endgroup$ – Benjamin Thoburn Nov 30 '18 at 15:56
  • $\begingroup$ Also if you have differentials you can sensably make a sort of derivative so the two words aren't even that different. However this is just how I remember it, Mikhail gives the real answer. $\endgroup$ – Benjamin Thoburn Nov 30 '18 at 15:56
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In French there is less of a problem with terminology: differentiation is called "dérivation", and derivative is, you guessed it, "la dérivée". The term "fonction dérivée" was originally introduced by Lagrange. The English term "differentiate" ultimately derives from "differences"; namely, Leibniz originally studied finite differences and discovered certain patterns that led him to introduce (infinitesimal) differentials.

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I believe the term "derivative" arises from the fact that it is another, different function $f'(x)$ which is implied by the first function $f(x)$. Thus we have derived one from the other. The terms differential, etc. have more reference to the actual mathematics going on when we derive one from the other.

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