Talk:Derivative

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After the definition is given, indications on how to read are given. They include

"dy by dx at a", or "dy over dx at a"

should it be

"df by dx at a", or "df over dx at a"

since "y" is not use in the section ? Padelsart (talk) 13:02, 1 February 2023 (UTC)Reply

  Done Chaged dy to f, and reworded a bit. Whether or not there are people who say "dy by dx" in this context, it is a confusing thing to include right after the definition, and should be kept to the notation section. small jars tc 18:01, 1 February 2023 (UTC)Reply

I think the formula from Stegun (https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf, page 824) should be added here: ${\displaystyle {\frac {d^{m}}{dx^{m}}}f(x)=m!\sum _{n=m}^{\infty }{\frac {s_{m}^{(n)}}{n!}}\Delta ^{n}f(x)}$  which contains the stirling numbers of the first kind and the forward difference operator to compute nth derivatives as series. Thoughts? — Preceding unsigned comment added by Onlineuser577215 (talk • contribs) 19:35, 21 September 2023 (UTC)Reply

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Researchrush (talk) 23:22, 28 September 2023 (UTC)Reply

I would like to add a brief bit about how Issac Newton called the derivative "the flowing quantity" and the notation he used.

  Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. JTP ^{(talk • contribs)} 00:02, 29 September 2023 (UTC)Reply

After my reversion of the change of the heading § Euler's notation, I received the Could you please provide any evidence on the edited page that Euler used or popularized the D-notation for derivative, or that it is a "common name" (among who?) Otherwise, could you please restore my edit? Alexey Muranov (talk) 12:07, 2 October 2023 (UTC).

I am unable to provide to decide which is the most common name among "Arbogast's notation", "Euler's notation", and "D-notation", but it is certainly not "Arbogast's notation". This justifies my revert. However, there are so many things that are named after Euler's, that "Euler's notation" would need, at least, to be disambiguated. So, I'll change the heading to "D-notation", with a template {{anchor|Euler's notation}} and a note on the attribution. D.Lazard (talk) 14:05, 2 October 2023 (UTC)Reply

@D.Lazard, I am not asking to you to decide, I am asking you to provide sources based on which you reverted my edit. Wikipedia should not invent names. A source that attributes the notation to Arbogast is currently cited in the very first sentence. You say something justifies your revert, but it is not clear what. Alexey Muranov (talk) 17:59, 2 October 2023 (UTC)Reply

Again, per Wikipedia usage, this is not the attribution which motivates the name; it is the common usage. This is the fact that "Arbogast's notation" and "Arbogast notation" are very uncommon (less than 20 hits in Scholar Google) that justifies my revert. D.Lazard (talk) 18:34, 2 October 2023 (UTC)Reply

Could you please provide a reference to the relevant statistics of Scholar Google which justifies the "Euler" name? Common usage by whom? How the statistics were collected? On the other hand, since it is Arbogast's notation, in the sense that he invented and popularized it, it is a sufficient reason to call it so. Alexey Muranov (talk) 20:04, 2 October 2023 (UTC)Reply

I am actually not sure if Google Scholar statistics should be considered a source for a terminology, but it will be better than nothing. Alexey Muranov (talk) 20:07, 2 October 2023 (UTC)Reply

I agree that Google Scholar must be considered with care. It is reliable for establishing that a terminology is uncommon. But it is not for comparing "D-notation" and "Euler's notation" because both phrases can have other meanings. Nevertheless "D-notation" seems less ambiguous. This is the reason for changing headings § Euler's notation to § D-notation. For avoiding reader's confusion, and not breaking the redirect Euler's notation (and other incoming links), I have kept an anchor, and added a sentence mentioning the attribution to Arbogast, and the alternative name of Euler's notation. D.Lazard (talk) 20:36, 2 October 2023 (UTC)Reply

Sorry, but could you then please provide any justification that "D-notation" is a "common usage"? By whom? And if you keep a redirect for "Euler's notation", could you please explain what makes you think that this is "Euler's notation" in any sense? Alexey Muranov (talk) 04:58, 3 October 2023 (UTC)Reply

I have absolute no opinion whether this is notation is due to Euler or not, and even whether Euler used it or not. The established fact is that many people use the phrase "Euler's notation" for naming this notation, and Wikipedia cannot change this fact, and must not try to change it. This is why, whichever is the name of the section, the redirect Euler's notation must be kept and have the corresponding section of Notation for differentiation as a target.

An title must be chosen for the section. "Arbogast's notation" is excluded because, it is very rarely used, and as such, choosing it would break the fundamental rules of Wikipedia, in particular WP:OR. So, you must chose between "Euler's notation", which is a common name for the notation, and "D-notation", which is a factual description of the notation. What is your choice? D.Lazard (talk) 08:58, 3 October 2023 (UTC)Reply

@D.Lazard, you say """The established fact is that many people use the phrase "Euler's notation" for naming this notation""" -- please justify by providing references. According to what statistics? Do they understand what they say? "Arbogast's notation" is ok as a title, since it is indeed a notation of Arbogast. This is not orignal research, this is a known fact. At least according the literature I checked. Alexey Muranov (talk) 20:19, 7 October 2023 (UTC)Reply

WP:CRITERIA gives 5 criteria for choosing the article title. Neither "Arbogast notation" nor "Euler's notation" satisfy the two first criteria of recognizability and naturalness. This is the reason for which I changed the heading (here and in Notation for differentiation) into "D-notation", that is both natural and easily recognizable. I have also added a sentence in the beginning of the section for attributing the notation to Arbogast, and saying that some authors (not "many") use improperly "Euler's notation". This improper use of "Euler's notation" must be mentioned since some people may search for it, at least those who learned it in Wikipedia, where it appeared in a edit of derivative of 8 August 2005‎. D.Lazard (talk) 10:55, 8 October 2023 (UTC)Reply

The Total derivative, total differential and Jacobian matrix section is awfully wordy and detailed for an article that's supposed to be about the concept of the derivative in general. It's a bit odd that we have 10 paragraphs of text that take up about 2 screens and invoke mappings between tangent bundles, but we don't have anything on maxima and minima of single-variable functions. And within that section, there's less emphasis comparatively speaking on Jacobians than I would have expected given how much I've seen these concepts covered in courses at different stages. XOR'easter (talk) 03:43, 16 December 2023 (UTC)Reply

If that's the case, maybe this section can be summarize in at least one, two, or three paragraphs? Also, most of them are unsourced, together with the usage of first-person pronoun. Dedhert.Jr (talk) 13:28, 17 December 2023 (UTC)Reply

I've trimmed it back to something more reasonable. It still needs sources. XOR'easter (talk) 17:25, 20 December 2023 (UTC)Reply

@XOR'easter I have found the source of the definition [1], but it seems likely different than the article. Hopefully this helps, and I will keep searching for more. Dedhert.Jr (talk) 01:48, 21 December 2023 (UTC)Reply

During GAR, I removed the hidden online sources while improving the article.

• Crowell, Benjamin (2017), Fundamentals of Calculus
• (Govt. of TN), TamilNadu Textbook Corporation (2006), Mathematics- vol.2 (PDF), archived from the original (PDF) on 2016-01-15, retrieved 2014-11-29
• Garrett, Paul (2004), Notes on First-Year Calculus, University of Minnesota
• Hussain, Faraz (2006), Understanding Calculus
• Mauch, Sean (2004), Unabridged Version of Sean's Applied Math Book, archived from the original on 2006-04-15
• Sloughter, Dan (2000), Difference Equations to Differential Equations
• Strang, Gilbert (1991), Calculus
• Stroyan, Keith D. (1997), A Brief Introduction to Infinitesimal Calculus
• The Notation of Differentiation, MIT, 1998, retrieved 24 October 2012
• Wikibooks, Calculus

All of these sources here are in the format CS2. Dedhert.Jr (talk) 04:48, 31 December 2023 (UTC)Reply

So at the end, you find the value which is the area of triangle multiplied by 2, not the surface area of triangle.

Matrix(A) . Transpose Matrix (A^-1) = 1. It is the agreed one as everyone knows of it. And the matrix concepts falls on the linear algebra & part of the mathematics

I have checked in the following link, that the slope of the line can be calculated like this as mentioned in the page,- https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope/a/slope-formula

I had tried a little permutation of the calculation myself, concluding putting it into a two dimensional matrix.

|x1, y1|

|x2, y2|

|1, 4|

|7, 7|

x1 = 1

x2 = 7

y1 = 4

y2 = 7

Slope => y2 - y1 / x2 - x1 => 7 - 4 / 7 - 1 => 3 / 6 => 1 / 2

If it is a Matrix

|x1, y1|

|x2, y2|

Slope => (x1 x y2) - (x2 x y1) => (1 x 7) - (7 x 4) => 7 - 28 => - 21 => 21

|x, y|

|x1, y1|

At the end I am missing my mathematics that how value been profound. Number 2 is important in the mathematics also in computer field act as binary base system. Not only that, however I am not able to recall, 2 is an important number in vectors, stating the surface is 2 even if the side values are just denoted by value which is equals to 1 and it is a vector. Even √2 is important. 45° is important as it gives bijection between x and y.

And as you found a value of delta / 2 is equals to surface of the triangle value, if the z-axis is intact and the field is just 2D, and as I somehow recalls, number 2 plays vital role in vectors, I feel I can connect 21 with 1/2.

I couldn't relate 1/2 with 21 by mathematics, and as however in all higher dimensional matrix also, A.A^T = 1. So I give all my chances to the serieses like harmonic series and the other ones. Other than that slope is always profound by derivative, a division of mathematics. And in vector 2 is important. And in matrix A.A^T = 1

Let's step into 3D not by 2D any more.

—BilkTheHulk ^{Talk - "Only dead fish go with the flow."} 20:25, 17 January 2024 (UTC)Reply

I moved this comment to a new section and archived the extremely stale 10-year-old comment it was nominally a "reply" to. I can't really make much sense of this new comment or figure out whether/how it was supposed to relate to the previous one in any way. –jacobolus (t) 23:31, 17 January 2024 (UTC)Reply

Mathematical solutions by method / formulas has limit by connecting one another way of having mathematical explanations for it and by the ways of mathematics. Before getting into higgs, science must evolve by this way, so physics gets into a better shape. I am little wise with chemistry and it has its own limit on its applicability, so it can ignored a bit when it goes beyond its context.

I was about to say something before, but got deviated. Here it is — the way how 2 is important and √2, i is less important I feel, I mean the √-1. From derivative, or by any different chapters of mathematics, we may indulge well but we should correct our context in all sense. So, let's get into mathematical proofing and our best logical augmentation in all aspects, so we will be in a position to face consequences by all sort, the good the FLAMINGO project is the best we survive or yield to the next—AtTEnigma^t@lk 19:45, 4 February 2024 (UTC)Reply

Sorry, but I do not understand what point you are trying to make. Please stick to concrete criticisms/suggestions about this article, and try to make your comments as clear as possible to help other editors follow along. Note that this talk page is not a general-purpose forum. –jacobolus (t) 00:48, 5 February 2024 (UTC)Reply

See first of all I don't know anything about Jacobian Matrix.

Even I couldn't understand anything out of it over here as they way been said over here "Not able to comprehend".

I think the guy simply says i² is equals to -1. And I think he doesn't believe mutlti-dimentional concepts.

Out the linearity and vector, we may have i to z, meaning i, j, k, l, m, n .. q ...,

And they way he believes it is either we may have to subtract instead. I mean instead of x² + y² having minus (-) here -> x² - y². Like how we have (a+b) x (a-b), and a, b - vector with same direction but the conjugate (a+ib) x (a-ib). Maybe I am wrong as I am not wise with Mathematics, it's simple someone easily correct & conclude so,

I also do not able to comprehend multi dimensional theory so far in my conceptual mind. So he maybe little clear. But in the wrong place Talk:Derivative. Anyway lets talk, nothing harm happens, I believe. Conclusion is final by philosophy or may be by me. Thanks!

—20:08, 29 May 2024 (UTC) BramStoker's^{Talk to me.} 20:08, 29 May 2024 (UTC)Reply

@D.Lazard: Edit Special:PermanentLink/1201066147 changes constants back to all real numbers. The reversion was appropriate because it was in the context of real functions of real variables. However, I believe that it would be appropriate to have a brief acknowledgement that the chain rule is more generally applicable. I'm not sure whether it would be better inline or as a footnote. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:00, 31 January 2024 (UTC)Reply

For applying the chain rule to a sum, a product or a fraction, one has to know the partial derivatives of a sum, a product or a division with respect to each of their arguments, and to use the chain rule for several variables. So, the proofs of these formulas using the chain rule are much more complicate (in the whole) than the direct proof. The mention of the chain rule in two variables is therefore too technical here. D.Lazard (talk) 16:33, 31 January 2024 (UTC)Reply

Agreed: I wasn't suggesting adding an exposition on anything beyond the case of a reals function of a single real variable, just adding a brief note that it generalizes. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:53, 31 January 2024 (UTC)Reply

(Aside: a link like special:diff/1201288095 will show the change in addition to the end state.) I think "real numbers" seems fine, since the context in this page is single-variable real functions. I think a more general discussion belongs at Linearity of differentiation which is where the wikilinked sum rule heading in this article points. –jacobolus (t) 16:52, 31 January 2024 (UTC)Reply

I was suggesting only a note that there was a more general chain rule, not a more detailed discussion.

Thanks for telling me about [[special:diff/oldid]] -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:53, 31 January 2024 (UTC)Reply

@D.Lazard: With regard to edit special:diff/, I wrote the term as used in calculus on the Real line, not the term as used on the Real line. Also, the article is not about the term as used in calculus on Euclidean spaces in general, but rather the special case of calculus on a one dimensional Euclidean space. Given that, This is about real functions, not about the real line does not explain the reason for the reversion. Would you accept {{about|the term as used in the calculus of real functions of a single real variable|derivatives on manifolds|covariant derivative|and|Lie derivative|generalizations|generalizations of the derivative|a less technical overview of the subject|differential calculus|other uses}}? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:34, 1 February 2024 (UTC)Reply

As said in my last edit, hatnotes are only for disambiguation, and must not duplicate the dab page and/or the infobox. So, for this article, the only acceptable hatnote is {{Otheruse}}. D.Lazard (talk) 17:43, 1 February 2024 (UTC)Reply

I believe that the lead should mention early on that there are several related notions referred to as derivative, e.g.,

1. The classical derivatives of real (complex)-valued functions of single real (complex) variables.
2. The covariant derivative
3. The Lie derivative

The lead shouldn't give a complete list, just enough to demonstrate the ambiguity. Shmuel (Seymour J.) Metz Username:Chatul 12:38, 6 August 2024‎ (UTC)Reply

Umm... if the problem is about the ambiguity meaning, why can't we just extend the usage of {{other uses}}? We may just explain this article is about the derivative in general calculus. Dedhert.Jr (talk) 15:43, 6 August 2024 (UTC)Reply

Or replace {{other uses}} with {{about}}? Which of these should be in the {{about}}?

• Covariant derivative
• Exterior derivative
• Functional derivative
• Lie derivative

Are there any others important enough to warrant a link in the {{about}}? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:31, 6 August 2024 (UTC)Reply

There is a page Derivative (disambiguation). So, none must be in an {{about}} or {{other use}} template. Instead to have many terms in a hatnote, these terms must be added in the disambiguation page, when there are not already there.

I've updated Derivative (disambiguation).

What about the related algebraic term derivation? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 10:48, 7 August 2024 (UTC)Reply

By the way, none of the listed terms is ambiguous, and there are all generalizations of the usual derivatives. So, they must be added in the generalization section (if they are not there) with some explanation of the relationship with usual derivatives. D.Lazard (talk) 09:19, 7 August 2024 (UTC)Reply

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—————

1F. Change from:

Repeated references to Gonnick 2012 (The Cartoon Guide to Calculus)—SIX appearances in the critical opening sentences of the article—

1T. Change to:

A reputable, scholarly secondary open source for the same material (with checking of content to new source, not just hot-swapping the citations).

—————

2F. Change from:

Repeated appearance of in-citation dead-end URLs in the opening 15 inline citations (rather than to true, article-supporting maths content; instead, links are to book sales sites, Wikipedia pages for the cited book, archive.org / google.com sites with no content presented, etc.)—

2T. Change to:

No links (square bracket or related markup removed), or an added disclaimer in the inline citation text noting the valuelessness of the link to the inline citation (see below), or replacement links that actually take readers to the suggested maths content supporting the text, or more carefully chosen replacement sources that make the useless inline citations and their links unnecessary.

Justifications:

General. Currently, at best 3 of the first 17 inline citations links are actually useful to readers, in that only the 3 convey readers to a separate site that either supports the content appearing (in support of WP:VERIFY), or presents further material allowing deeper explanation and understanding. Please check this 3 of 17 contention; we maintain that useful links do not appear before inline citation [9] to Keisler 2012, and thereafter they revert again to being useless (at least for a time). This density of poor sources at the top of the article indicate us a top down, post hoc attempt to provide any source at all for content earlier created but unsourced. (It also suggests a dedicated period of bibliographic work, wherein presenting bad links within the citation was perceived as being better than presenting no link at all, for these critical opening paragraphs of the article.)

Specific justification, (1) Given the wealth of scholarly web material on basic mathematics, there is no reason to use cartoon guides to STEM content—certainly not as a preponderant source in the opening definitions of this fundamental maths article (Gonick is a maths citation that belongs, at best, in the Further reading section.) Its appearing both does a disservice to readers, pointing them toward a source that is not being used in formal maths education, and then a disservice to the encyclopedia, creating a sense of less-than-seriousness-of-approach, at the beginning of this very important article. As noted, use of this source appears to have been the result of dedicated period of naive, rather than academically informed editing.

Specific justification, (2) Presenting URLs for any citation that takes a young academic reader nowhere of value, e.g.—

= Stewart 2002, to a front matter-only page at archive.org [despite our being registered], 
= Strang et al. 2023, to a book sales site, 
= Thompson 1998, just to the book's Wikipedia page, not to any of its content,
= Etc.—

is a disservice to readers, in that it distracts and disorients, and so wastes valuable educational time; and again, it casts the encyclopedia in an ill light. The links to sales sites should clearly be verboten. I would also say the remaining sites should also not appear, or that their inline citations should be accomplanied by a disclaimer that stops the reader from clicking on the useless link. ("The links appearing in the preceding citation identify the book but otherwise contain no accessible content relevant to the material presented in this Wikipedia article.")

An alternative to all of the above is that the the article be returned to a lower restriction level, to allow for open scholarly editing (realizing that such comprehensive, even if specific, changes noted are burdensome). But it is not in our power to change the protection status of the article, or editorial perspective that sidelining dedicate, good editors is a reasonable cost for avoiding the hassles of reverting vandalism. (But note, there are easily applied tools to ID likely vandalism; it is not possible, yet, to improve the article, as I ask, apart from skilled editors such as the two of us. And as we cannot, we must ask you.)

Bottom line, we can only see the issue of a locked-in-as-weak article, and do nothing about it except write these long requests.

Signed, a former prof, and former registered editor here. 98.193.42.97 (talk) 21:31, 7 September 2024 (UTC)Reply

Apologies, but we do have a guideline WP:RS, stating a reliable source consisted of author, year of publishing, and reliable publisher. Dedhert.Jr (talk) 00:41, 8 September 2024 (UTC)Reply

  Not done Edit requests should have the form "please change X to Y"; if you would to suggest particular source substitutions (in a concrete way, by proposing the concrete addition of a specific reference in a specific location), you are welcome to do so. --JBL (talk) 00:55, 8 September 2024 (UTC)Reply

Can you be more specific about which source you would prefer? If you would like, feel free to copy wikitext to the page Talk:Derivative/Sandbox I just created, where you can work on draft changes. (Or create an account so you can edit any semi-protected page you like.) –jacobolus (t) 01:47, 8 September 2024 (UTC)Reply

Materialscientist protected this page back in 2021 in response to a bout of vandalism by IP editors. @Materialscientist would you consider un-protecting the page, and we can see if the vandals might have given up by now? It's not clear to me why this page should be permanently protected against anonymous editing. –jacobolus (t) 01:50, 8 September 2024 (UTC)Reply

(2) Presenting URLs for any citation that takes a young academic reader nowhere of value – Citing physical books seems unproblematic to me, and Stewart's is one of the most popular. A reader who wants to verify the claims made or see more can easily find this book in their local public or school library. For internet archive book links to copyrighted sources, you may need to first "check out" the book before reading the content, hence the gray dotted lock icon, or for some books publishers have requested that the content not be visible at all (such links should probably be removed, leaving link-less citations or e.g. linking Google Books instead). But since this is a very old and static topic, we could certainly also link to freely available scans which would be just as good. For example we could link to Goursat (1904) A Course in Mathematical Analysis, Courant (1937) Differential and Integral Calculus, Piskunov (1969) Differential and Integral Calculus or even Lacroix (1816) An Elementary Treatise on the Differential and Integral Calculus. –jacobolus (t) 02:10, 8 September 2024 (UTC)Reply

What exactly is wrong with citing a book by an author who studied mathematics at Harvard and has spent decades writing and co-writing well-regarded expositions of science, mathematics, and history? XOR'easter (talk) 06:11, 8 September 2024 (UTC)Reply

There are much better sources available. For example, the epsilon delta definition of a limit should be cited to a standard textbook on analysis, such as Bartle. Tito Omburo (talk) 18:29, 8 September 2024 (UTC)Reply

I don't think the only source for a fact that is encountered well before a course on real analysis should be a textbook on real analysis. XOR'easter (talk) 20:57, 8 September 2024 (UTC)Reply

How about Calculus texts such as Thomas^[1] that go into Epsilontics? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:00, 9 September 2024 (UTC)Reply

Strang et al. 2023 is not a "book sale site"; it's a free online textbook that offers the option of buying a print copy. XOR'easter (talk) 22:18, 9 September 2024 (UTC)Reply

There id no need for this article to be protected. 107.119.57.63 (talk) 21:36, 20 September 2024 (UTC)Reply

• is

107.119.57.63 (talk) 21:37, 20 September 2024 (UTC)Reply

The article's edit history shows the data of edit-warring by some IPs and users. That is why the article is protected. Dedhert.Jr (talk) 03:41, 21 September 2024 (UTC)Reply