Talk:Derivative at a point: Difference between revisions
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imported>Boris Tsirelson (→Derivative: I never met the term "differential quotient") |
imported>Peter Schmitt (→Derivative: just not used/observed, or a Germanism?) |
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::OK, I see your point. But as the article reads now, it only confuses the reader further as to the difference between the derivative and the d.q. [[User:Johan A. Förberg|Johan A. Förberg]] 23:34, 22 January 2011 (UTC) | ::OK, I see your point. But as the article reads now, it only confuses the reader further as to the difference between the derivative and the d.q. [[User:Johan A. Förberg|Johan A. Förberg]] 23:34, 22 January 2011 (UTC) | ||
::: I never met the term "differential quotient". Wikipedia has no such article, and moreover, its search gives no results. Google gives first 5 results that contain in fact only "difference quotient", but result no. 6 (dictionary.com) mentions "differential quotient" as item 6 in "derivative". --[[User:Boris Tsirelson|Boris Tsirelson]] | ::: I never met the term "differential quotient". Wikipedia has no such article, and moreover, its search gives no results. Google gives first 5 results that contain in fact only "difference quotient", but result no. 6 (dictionary.com) mentions "differential quotient" as item 6 in "derivative". --[[User:Boris Tsirelson|Boris Tsirelson]] 0:34, 23 January 2011 (UTC) | ||
:::: Yes, I was also surprised that it popped up so rarely, but it does so in different places, including research papers. | |||
:::: Could it be a Germanism? The term is very usual in German. I'll try to find out more in the literature -- old and new. This may help to deal with it properly. | |||
:::: From a didactical perspective, it is a rather useful distinction -- e.g., you need a derivative (function) before you can talk about s second derivative. | |||
:::: --[[User:Peter Schmitt|Peter Schmitt]] 10:58, 23 January 2011 (UTC) | |||
Revision as of 04:58, 23 January 2011
Derivative
Peter, could you please explain why you prefer the title "differential quotient"? I haven't studied mathematics in English for some time, but I still feel that "derivative" is the more common name. Formally, the derivative should be the limit of the differential quotient as h approaches zero, but in my mind they are not the same concept. Johan A. Förberg 22:08, 21 January 2011 (UTC)
- I see a subtle difference:
- The differential quotient of f at x is the limit of the difference quotients at x (only one particular point considered),
- while the derivative of f is the function with values equal to the differential quotient (the full dominion of the function is considered).
- (The redirect is not final, "derivative" should have its own page, as should have "derivation".)
- Peter Schmitt 00:54, 22 January 2011 (UTC)
- OK, I see your point. But as the article reads now, it only confuses the reader further as to the difference between the derivative and the d.q. Johan A. Förberg 23:34, 22 January 2011 (UTC)
- I never met the term "differential quotient". Wikipedia has no such article, and moreover, its search gives no results. Google gives first 5 results that contain in fact only "difference quotient", but result no. 6 (dictionary.com) mentions "differential quotient" as item 6 in "derivative". --Boris Tsirelson 0:34, 23 January 2011 (UTC)
- Yes, I was also surprised that it popped up so rarely, but it does so in different places, including research papers.
- Could it be a Germanism? The term is very usual in German. I'll try to find out more in the literature -- old and new. This may help to deal with it properly.
- From a didactical perspective, it is a rather useful distinction -- e.g., you need a derivative (function) before you can talk about s second derivative.
- --Peter Schmitt 10:58, 23 January 2011 (UTC)