Talk:Notation for differentiation

message: There is more to be done here. but I made a start, and hope I have made all the redirects work correctly. Geometry guy 23:25, 25 March 2007 (UTC)
thread_title: Initial page

message: I think this page is lacking the simplest, first day of calculus, notation where you approximate a derivative using a small delta. In other words, we need \frac{\Delta y}{\Delta x}. 
I was hoping to see all 3 fraction styles here \frac{d y}{d x}, \frac{\Delta y}{\Delta x}, and \frac{\partial y}{\partial x}, with an explanation for when to use each.
The rules are that the delta style (the missing one) is the numerical approach where you then take the limit as the delta goes to zero. The non-script d is for a single-variable function, and the script \partial is for a multi-variable function. 
I think the delta-style (whatever you call it) is necessary to show since (1) it's a valid means to express a derivative, (2) it's a very common notation used when teach derivatives, and (3) it'll complete the picture painted on this page. 
Hey.Dr.Nick (talk) 15:58, 6 January 2021 (UTC)
thread_title: Missing Numerical Notation

message: * Partial derivatives should be introduced prior to using them under vector calculus.  Right now, they aren't "defined" until the end of the article.
* There is no mention of mixed partials currently.  This is important because I came to this page trying to see how to "read" the order of the derivatives.  For example, does \frac{\partial^2f}{\partial x \partial y} = f_{xy} mean "the derivative of f with respect to x then with respect to y" or vice versa? Kdmckale (talk) 17:35, 10 August 2010 (UTC)
replies: text: * That's the same reason I was reading the article. The answer can be found in the article Partial derivative: \frac{\partial^2 f}{\partial y \, \partial x} = \frac{\partial}{\partial y} \left( \frac{\partial f}{\partial x} \right) = f_{xy} = \partial_{yx} f. Note that in many cases it doesn't matter, see Symmetry of second derivatives. Paul Breeuwsma (talk) 20:01, 7 December 2010 (UTC)

text: Funny - just switched the sections around before reading your post and writing that I did so on this talk page... M∧Ŝc2ħεИτlk 08:19, 26 March 2013 (UTC)
thread_title: Future work

message: Some books on PDE use the following notation in first and second order PDE:
p=z_x, q=z_y, r=z_{xx}, s=z_{xy}, t=z_{yy}.
I have no idea where this notation originated, or how common it is. Hadaso (talk) 07:17, 25 October 2013 (UTC)
thread_title: p,q,r,s,t Notation

message: The following is without reference and is not commonly used:
::the use the nabla operator using subscripts to indicate the variables with respect to which the function is being derived:
:::     \nabla_t f = \frac{\partial f}{\partial t}. 
I am going to take it away from the article. Bo Jacoby (talk) 11:14, 23 September 2014 (UTC)
thread_title: uncommon notation

message: I have no idea why a section on notation for integration has been added. We already have an article for that: Integral symbol. The section talk:Notation for differentiation#Newton's notation for integration should be moved over there. M∧Ŝc2ħεИτlk 15:50, 5 February 2016 (UTC)
thread_title:  Notation for integration 

message: Substituted at 02:24, 5 May 2016 (UTC)
thread_title: Assessment comment

message: The notation of differentials, derivatives etc. is also standardized in ISO 80000-2 Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology (this title is intended to be shortened to read “Mathematics” in a future edition.) and other related international and national standards. This reference and the conforming notation and typography should be included in the article.
– Emeldir (talk) 13:05, 16 January 2017 (UTC)
replies: text: In the past, ISO's mathematical typography has always struck me as uninformed, amateurish, and ugly. Moreover, their prescriptions are never used within pure mathematics and are not consistently used within applied mathematics. While it may be necessary for this article to mention ISO, I feel like it would be undue weight to include more than a brief paragraph. Ozob (talk) 18:38, 16 January 2017 (UTC)

text: I personally prefer the upright d for derivatives yet I see we have used the italicized version here for this article. Most people in my department (Applied Mathematics) use the upright d, as well as the pure maths department upstairs. Is there a specific reason why the italic d was used for this article. Kendall Born (talk) 07:38, 3 December 2019 (UTC)
replies: text:  I find that italic d is used more by pure mathematicians while roman d is more often used by physicists, engineers, and applied mathematicians. (There are exceptions in either direction, of course.) Since this article is about a mathematical topic, I think it makes more sense to use the stye from pure mathematics. That said, the roman style deserves a mention, which I've added. Nloveladyallen (talk) 05:40, 4 December 2019 (UTC)
thread_title:  International Standards 

message: I'm not sure why we need the boxes on the right-hand side illustrating the use of each notation. Each notation is already demonstrated in its respective section, so the boxes are redundant, unless your attention span is so poor that you can't read the article text, and need everything important in VERY LARGE FONT.
If we are going to keep them, they should at least be set in TeX. The HTML versions are extremely ugly, at least on my machine. Nloveladyallen (talk) 05:56, 2 December 2019 (UTC)
thread_title:  Boxes on the right-hand side 

message: See: https://hsm.stackexchange.com/a/7409/3462
This should be reflected in the article.  — Preceding unsigned comment added by Mbachtold (talk • contribs) 10:54, 20 December 2020 (UTC)
thread_title:  Lagrange's Notations is actually due to Euler 

message: The rationale given for higher-order derivatives is that it's from "formal manipulations of symbols", i.e. 
:\frac{d\left(\frac{dy}{dx}\right)}{dx} = \left(\frac{d}{dx}\right)^2y = \frac{d^2y}{dx^2}.
But as any junior high school algebra student knows, it should be
:\frac{d\left(\frac{dy}{dx}\right)}{dx} = \left(\frac{d}{dx}\right)^2y = \frac{d^2y}{(dx)^2}.
What was Leibniz thinking? jej1997 (talk) 07:59, 8 March 2024 (UTC)
replies: text: In this context,  is not a variable and must be seen as the symbol of a function. Thus  dx must be interpreted as d(x), and both  dx^2 and (dx)^2 must be interpreted as d(x)^2=(d(x))^2. At Leibniz time, the functional notation was not yet fixed, and the parentheses around the argument of the argument of a function were not systematic. For example, one writes still \sin x instead of \sin(x). D.Lazard (talk) 09:34, 8 March 2024 (UTC)
thread_title:  Was Leibniz bad at algebra?