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I have encountered the term derivate standing in for derivative many times in posts. I usually edit the post to say derivative instead. But I am wondering, are their regions of the world where the term derivate is used instead?

Note: I mean when used as a noun. But that does bring up another question. Instead of using derivate as a verb, I would use differentiate. Again, perhaps the former is common practice in regions.

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    $\begingroup$ isn't "derivate" a (conjugated) verb and "derivative" a noun? (I'm not native english spear).¨ $\endgroup$ – Surb Jun 30 '15 at 14:35
  • $\begingroup$ @Surb Thanks. I clarified the question was regarding when it's used as a noun. $\endgroup$ – muaddib Jun 30 '15 at 14:40
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    $\begingroup$ Well then, personally, I never encountered "derivate" as a noun in any official literature. $\endgroup$ – Surb Jun 30 '15 at 14:41
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    $\begingroup$ @Surb "Derivate" seems only like a noun to me, and the dictionary seems to confirm. "Derive" is the root verb... $\endgroup$ – rschwieb Jun 30 '15 at 14:43
  • $\begingroup$ @rschwieb, does "salivate" seem like a noun? See this question for an example where "derivate" is (mis)used as both noun and verb. $\endgroup$ – Barry Cipra Jun 30 '15 at 19:43
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    $\begingroup$ Wouldn't this be an acceptable question on the main (non-meta) site? $\endgroup$ – rabota Jul 1 '15 at 18:10
  • $\begingroup$ @BarryCipra no, salivate does not seem like a noun since I know that it is the root verb. "Salive" is a bogus English word, it seems, so there is no similarity beyond the one you mentioned. In some cases, the extension is used on a word that is both noun and verb, like "advocate." Using the root verb seems to be the handiest way to distinguish. $\endgroup$ – rschwieb Jul 5 '15 at 3:20
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For what it's worth, this is from page 89 of Whittaker and Watson (A Course of Modern Analysis, 1946 "American" edition):

The function $f'(z)$, which is the limit of

$$f(z+h)-f(z)\over h$$

as $h$ tends to zero, is called the derivate of $f(z)$.

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Although the word "derivate" is sometimes used intentionally in English as mentioned in the other answers, it may also arise unintentionally through a similar word in the OPs native language (or the language they have studied math in). In Finnish derivative is "derivaatta", which makes it natural for Finnish students to translate it to English as "derivate". Similarly "to differentiate" is "derivoida", which suggests a translation "to derivate" back to English. I would guess that a similar thing can happen with other languages as well.

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    $\begingroup$ In Spanish you have the verb "Derivar" and noun (actually a past participle) "Derivada". A careless translation of the latter would give you something between derivate and derived. $\endgroup$ – Pedro Sánchez Terraf Jul 4 '15 at 23:14
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    $\begingroup$ Pedro's comment also goes for Portuguese. $\endgroup$ – Ivo Terek Jul 9 '15 at 19:20
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    $\begingroup$ It's pretty much the same thing in Italian. We have the verb "derivare" and the noun "derivata" (also a past participle). $\endgroup$ – rubik Jul 10 '15 at 7:31
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I have seen the "left/right derivate" defined as it is used here

I could swear I picked it up in Royden, but I can't confirm at the moment. Anyhow, this means you should be careful where you change the term. Sometimes it may indeed be used incorrectly for "derivative."

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    $\begingroup$ I wouldn't count examples from nonnative English speakers (the citation is to a book translated from Japanese to English by its author) $\endgroup$ – Bill Dubuque Jun 30 '15 at 18:07
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    $\begingroup$ And many of those also appear to be nonnative speakers. I am a native (USA) English speaker and I have never seen "derivate" used that way (it sounds quite strange to me). It is possible that is was used in older English textbooks, and when they started becoming available on the web, this caused the term to be used again. Further Google searches should reveal more. $\endgroup$ – Bill Dubuque Jun 30 '15 at 18:28
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    $\begingroup$ The third edition of Royden's Real Analysis calls the four values $D^+ f(z)$, $D^- f(z)$, $D_+ f(z)$, $D_- f(z)$ from your link derivates (although the definitions are slightly permuted). See p.99 of that edition. (I am uncertain about any other edition.) $\endgroup$ – user642796 Jun 30 '15 at 18:38
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    $\begingroup$ Dear @BillDubuque : The apparent intention of your emphasis that non-native speakers are using this term is to imply that it may in fact be incorrect. It seems you adamant about this despite the existence of many native writers also using it, and on top of it all, it seems all speakers are using it consistently to mean the same thing. I do not think the absence of your personal experience with it amounts to as much as you feel entitled. The objective conclusion from the data we have is that the usage in the cited passage is a real thing, not to be ruled out by author nationality. Regards. $\endgroup$ – rschwieb Jun 30 '15 at 19:12
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    $\begingroup$ @ArthurFischer, I have a second edition Royden, and the same derivates appear there on page 96. $\endgroup$ – Barry Cipra Jun 30 '15 at 19:18
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    $\begingroup$ @rschwieb I merely gave my experience as a native (American) English speaker. The OP can easily determine usage by doing the obvious Web searches. A proper answer requires much more than the single link you gave to a textbook translated from Japanese. Hence my remark. $\endgroup$ – Bill Dubuque Jun 30 '15 at 19:18
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    $\begingroup$ Dear @BillDubuque : By digressing into borderline ethnophobic comments ("I wouldn't count examples from nonnative English speakers") you did more than "merely give your experience." In any case, the question asks about usage "in regions of the world," so this opens the data to much more than American dialect. Regards $\endgroup$ – rschwieb Jun 30 '15 at 19:28
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    $\begingroup$ @BillDubuque A proper answer requires much more than the single link A single link sufficed for me since it had exactly the definition I had in mind, and matched all the other links I tried. I merely gave my experience with the term via a single illustration at hand. It would be more thorough to provide more links, but not altogether necessary, I think. Regards $\endgroup$ – rschwieb Jun 30 '15 at 19:30
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    $\begingroup$ @rschwieb I think you miss my point. This might possibly be a case where nonnative speakers have (inadvertently) revived an old or obscure usage. These things happen not too infrequently. To determine it that is true, one needs to perform a very careful analysis. A single link will not suffice. In particular, one needs to distinguish between native vs. nonnative usages, analyze timelines, etc. $\endgroup$ – Bill Dubuque Jun 30 '15 at 19:58
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    $\begingroup$ I'm having a lot of trouble differentiating the terms here. $\endgroup$ – James S. Cook Jul 4 '15 at 23:51
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    $\begingroup$ @James S. Cook: This comment is derivative of yours. $\endgroup$ – Jonas Meyer Jul 5 '15 at 0:06
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    $\begingroup$ @JonasMeyer If we were able to keep making derivative comments indefinitely, could we say we are smooth talkers? $\endgroup$ – rschwieb Jul 5 '15 at 3:02
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    $\begingroup$ Dear @BillDubuque : Since it is more or less transparent now that this grasping at straws in your last comment is a smokescreen meant to derail a conversation not going your way, I can't continue the thread. If you can disengage your targeting sights from me, maybe one of the other answerers would be interested in timeline analysis with you. Cheers $\endgroup$ – rschwieb Jul 6 '15 at 14:31
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    $\begingroup$ @rschwieb My prior comment is quite serious (and is already supported by an answer).The only straws visible here are your strawmen arguments. For once, could you please keep your comments on-topic, logical, and non-hyperbolic.. $\endgroup$ – Bill Dubuque Jul 6 '15 at 15:47
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    $\begingroup$ @BillDubuque dear, it is raining strawmen again. Ironic and hypocritical as your desperate accusations are, I will definitely not take your bait. Good day. $\endgroup$ – rschwieb Jul 9 '15 at 2:45

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