Talk:Implicit function

message: I added the "Formula for two variables" section a while back. Now I see that the triple product rule article essentially derives the same thing. Should I remove it and link to that article? --Spoon! 23:41, 31 August 2006 (UTC)
replies: text: I added a brief definition.  siℓℓy rabbit (talk) 02:00, 8 December 2008 (UTC)
thread_title: Discussion

message: The implicit function theorem doesn't really fit here, and deserves its own page.  Dfeuer 17:14, 7 October 2007 (UTC)
replies: text: I tend to agree. However I think the theroem is important enough to deserve a short overview section as in WP:SUMMARY. --Salix alba (talk) 22:48, 15 October 2007 (UTC)
thread_title:  Splitting [[Implicit function theorem]] back out. 

message: Thanks for the copious listing (and for transcribing the EOM reference---I couldn't get the link to work). I'm not sure about the Spivak reference. (When I mentioned Spivak, it was his Calculus, not Calculus on Manifolds, which I don't have next to me right now.) I concede the currency of the general term "implicit function." But note, still, how many of the references use it as a general term, but do not give it a specific definition. (The EOM being an exception, of course, and that's probably the best source to use.) That's not accidental; I think it's a reflection of how slippery the term is, and the fact that authors don't want confusion about the crucial term "function". 
Anyway, I'm still not happy with the phrasing in the article, which characterizes an implicit function as a special kind of function. The logic still doesn't make sense. I'd like it to be clear that you cannot say "Let f be an implicit function..." or ask "Is f an implicit function"? (As opposed to, say, "f is a function implicitly defined by R(x,f(x))=0", which is clearly meaningful.) Maybe the modification necessary is more minor than I first thought, something like:
:Formally, a function f:X→Y is said to be an implicit function (defined by the equation R(x,y)=0) if it satisfies the equation
::R(x,f(x)) = 0
:for all x∈X.
That brings R into the definition. An analogy: it doesn't make much sense to say "p is a characteristic polynomial", but it does make sense to say "p is the characteristic polynomial of the matrix A". 
Also, a quick glance at the Google Scholar results seems to indicate that there are at least three usages: (1) the EOM usage; (2) the function R, not the function f derived from it; (3) the phrase "implicit function surface" comes up (as a synonym for "level set of R", I believe). If that holds up, it seems necessary to address at least the first two uses.  
Yeah, I'm still being picky. I don't want to be annoying, but this is still bugging me. -- Spireguy (talk) 02:33, 2 May 2008 (UTC)
thread_title: Comments on sources

message: I believe this is a distinct topic that requires its own article. What do people think about a mergeout of this section? —Anonymous DissidentTalk 12:57, 26 May 2009 (UTC)
replies: text: It does seem that the way the article is now implicit differentiation gets lost in the shuffle. I'm not sure that creating a new article is the best solution but there needs to be some changes.--RDBury (talk) 12:08, 25 September 2009 (UTC)
replies: text: I dont know about a separate page, either, at least not until the existing section gets fleshed out. I can suggest some changes and additions to the first part. For example, the following sentence could be changed to clarify a bit: "It is impossible to express y explicitly as a function of x and dy/dx therefore this dy/dx cannot be found by explicit differentiation." (ie, moving the dy/dx term, striking 'this') I'm a bit rusty with explaining this in writing, so I hope the change leaves an accurate statement. -PrBeacon (talk) 02:45, 7 October 2010 (UTC)
thread_title:  Implicit differentiation 

message: I was confused by why x^2+y^2=1 is not a function and this article helped me to understand that a relation can be made for one or more implicit functions. https://math.dartmouth.edu/opencalc2/cole/lecture24.pdf  — Preceding unsigned comment added by 201.216.244.17 (talk) 18:22, 1 September 2015 (UTC)
thread_title:  I liked this article 

message: I would like to reintroduce the idea that implicit differentiation should have its own article. Why do all the integration techniques have their own articles but a differentiation technique doesn't?
JJPMaster (talk) 17:38, 28 March 2020 (UTC)
replies: text: It would be extremely difficult to split the article, as inplicit differentiation is fundamental for the definition of an implicit function (see the section "Implicit function theorem". Moreover, this article is rather short. So splitting it would not be useful. D.Lazard (talk) 22:56, 28 March 2020 (UTC)
thread_title:  Implicit differentiation should have its own article 

message: Hello! I don't have the time (or mathematical acuity to produce anything decent), but I would like it if there was a section describing how implicit equations are used to describe curves/surfaces in the euclidean plane/space (and possibly more). It could provide a short comparison with parametric/explicit equations, and link to the relevant articles (there is already a link at the bottom of the page for "implicit curve", but that's the extent of it).
Just thought I'd leave this here for people looking to contribute.
Ldorigo95 (talk) 13:20, 11 October 2020 (UTC)
thread_title:  Mention (and possibly link to relevant articles) how implicit functions behave when plotting