Talk:Derivative/Archive 1

message: funny trying to define "derivative" without used the phrase "derived from"??
--(talk)BozMo 19:58, 15 May 2004 (UTC)
thread_title: Funny

message: I believe that a critical number of f(x) also happens when f '(x) is undefined, not only when it is equal to zero.
:I second that.
:GTBacchus 05:21, 2 Dec 2004 (UTC)
thread_title:  Critical Numbers 

message: From the secion "Using Derivatives to Graph Functions":
"Additionally, the supremum of a continuous function on an open and bounded domain will also be one of the local maxima; the infimum will be one of the local minima--this gives one an easy way to find the bounds of the function's range."
I'm deleting this sentence.  Counterexample: the function e^x on the open interval (0,1).  Its supremum is e and its infimum is 1, but neither is a critical point.
:Neither is a critical point, but both are local extrema, right?  so how does that contradict the sentence? -Lethe | Talk 19:00, Jan 8, 2005 (UTC)
:It's probably better to correct the sentence than delete it. --Elektron 16:23, 2004 Jun 30 (UTC)
::If you can correct that sentence without making it 3 times longer, go for it. GTBacchus 18:00, 2 Jul 2004 (UTC)
thread_title:  deleted sentence 

message: On my computer, f prime looked like an f. If I looked really close, I could tell that the f that was really an f prime had a more rounded top than an f that wasn't prime. But anybody who can't read fine print any better than my wife can't see that, and the rest of us wouldn't notice either if we weren't expecting it. Maybe other people's fonts don't have that problem, but all I can do is fix the problem I can see here. 
So I put a space between the f and the prime. It doesn't look perfect - the prime is more lost with an f than it is with a g - but at least it won't cause a computation error.
Putting a space between the f and the prime doesn't work when the formula is inside those <mmath> thingies (mmath mispelling intentional to prevent it from formatting my text) in the Algebraic Manipulation section. But most of the formulas look the same with or without the <mmath> thingies. So I took them off in many places. But not in all places, because exponents don't work without the <mmath>'s. My conclusion was to take off some of the <mmath>'s but not all of them. The result is even more funny looking than the f prime/g prime problem, but at least it won't cause a computation error like the previous version would have. Art LaPella 06:49, Sep 2, 2004 (UTC)
Since then I reported the problem as a bug, and got this answer: "This is a problem with the specific fonts your browser is displaying and has nothing to do with MediaWiki or the site configuration." That's imaginable, except I don't know enough to monkey with fonts, so many of you may have the same problem. On my wife's computer f prime doesn't look like an f, but it looks like f square, which is almost as bad. Look at prime (symbol) and see if the f prime looks like an f. If so, Wikipedia presumably has lots of f primes that look like f's. Art LaPella 20:14, Sep 2, 2004 (UTC)
That's definitely your browser's choice of fonts. Pick a different font. On OSX, the prime is too low (the top of the prime is below the top of the f), but otherwise it's fine. If I change the font to Times, the italic f is too italic so the prime is stuck to it. This is a problem with OSX's renderer (though properly aligning italic text beside normal text has always been a problem). Either way, catering for rendering bugs isn't a good habit to get into. Elektron 13:35, 2004 Nov 1 (UTC)
Of course, we could change it back to an italic apostrophe, which probably renders more correctly but is even more incorrect (in Unicode, anyway). Elektron 13:41, 2004 Nov 1 (UTC)
Wouldn't it make sense to put the math tags back in, and display math as a PNG for those who have problems? I suspect Art LaPella would have to do this manually for his user, or move "formulas that have primes" to the category of formulas which should use PNGs by default (which the WikiMedia people may be reluctant to do), but that makes (IMHO) more sense than violating Unicode and WikiMedia standards for the benefit of someone with a poor choice of fonts (which may be a poor choice on the part of whoever developed the browser, I'm not blaming anyone, it just doesn't seem to matter to me). Roie m 12:18, 2 Dec 2004 (UTC)
thread_title:  f prime 

message: One should charitably assume that the statement
:"Functions do not have derivatives at points where they have either a vertical tangent or a discontinuity."
means that if a Function has a discontinuity or a vertical tangent then it is not differentiable; the converse of course is false.  Shouldn't this be made clearer, since many readers are likely to be much less eager to rely on principles of charity.
Also could the word "embodies" used in the phrase
: "a derivative embodies in terms of mathematics a rate of change"
occuring in the introduction be be replaced by something indicating more precisely the relation between the derivative and the rate of change? CSTAR 01:20, 8 Jan 2005 (UTC)
thread_title:  Ambiguous statement 

message: What exactly does this section add? Wouldn't it be enough to say that the derivative of f at c is also the same as
: \lim_{x \rightarrow c} \frac{f(x) - f(c)}{x - c}.
CSTAR 05:57, 8 Jan 2005 (UTC)
thread_title: The alternative difference quotient

message: I propose initially at least three illustrations:
1. One similar to the  picture illustrating the secant that is already there
2. One picture illustrating the tangent
3. One picture illustrating the tangent as a limit of secant
These illustrations would all be in the same style and moreover, new ones could be easily produced from the XFIG sources.
Other possible pictures include
* illustration of 
: \frac{\Delta y}{\Delta x}  
* illustration of convexity and concavity.
CSTAR 03:04, 7 Feb 2005 (UTC)
replies: text: I think the first three should be good idea. The one about convexity and concavity, that is badly needed on the Convex page. I am not sure about the last one,  \frac{\Delta y}{\Delta x} .  Oleg Alexandrov 04:25, 7 Feb 2005 (UTC)
thread_title:  Suggestions for pictures 

message: I support Oleg's revert action. Dmharvey  Talk 16:55, 10 August 2005 (UTC)
replies: text: I second the support of Oleg. I know how important it is in Wikipedia to fell validated :) --CSTAR 17:04, 10 August 2005 (UTC)
thread_title:  After Oleg's reversion 

message: In the first instance of \dot x \;, where all the different ways of expressing f(x) are discussed, shouldn't it be \dot f \; instead?  Note that further down in the article, the function \frac {dx}{dt}\; is expressed as \dot x \; instead of \dot t \;.  (Not an expert here, forgive me if I'm wrong!) Agent Zero 19:34, 9 August 2005 (UTC)
replies: text: you are correct --MarSch 18:03, 25 September 2005 (UTC)
thread_title:  Definition of "x-dot" 

message: Where would be the correct place to discuss
:(L_a f)(x) := f(x+a)
:f' := \lim_{a \to 0} \frac{L_a f - f}{a}?
this notation could also make the proof of the product rule more readable.
--MarSch 13:10, 28 October 2005 (UTC)
replies: text: I have no idea where to put that. The section on notation in this article is already too big, with three subsections, etc. I would suggest trimming it a bit. Oleg Alexandrov (talk) 13:33, 28 October 2005 (UTC)
thread_title:  operator notation 

message: Shouldn't the article Derivation (abstract algebra) be merged into this article? Jon Harald Søby \ no na 07:07, 4 November 2005 (UTC)
replies: text: No, I think at great length, it's been decided to keep this article just for the simple derivative of a real function in one variable.  See the scope section above. -Lethe | Talk 10:34, 4 November 2005 (UTC)
replies: text:  Agree with Lethe. Maybe something about derivation (abstract algebra) be said in derivative (generalizations) instead. Oleg Alexandrov (talk) 16:41, 4 November 2005 (UTC)
replies: text:  It's already there, in the Algebra section. Dmharvey  Talk 01:04, 5 November 2005 (UTC)
replies: text:  Thanks, I should have checked first. Oleg Alexandrov (talk) 01:45, 5 November 2005 (UTC)
thread_title: Merge

message: The article states that critical points are where the derivative is undefined or zero, and that local extrema only occur at critical points.  But clearly functions on the unit interval can have local extrema at their endpoints, and the derivatives can be nonzero and defined there, using one-sided limits.  The statement as it stands is therefore wrong, but I'm unsure as to whether the correct remedy is to allow boundary points of the domain to be critical points, or to change the result to say that extrema occur at critical points or boundary points. -lethe talk 23:54, 3 January 2006 (UTC)
replies: text: Personally, I'd go for the latter definition.  It looks like the section we currently have only considers functions on the entire real line.  —Ilmari Karonen (talk) 23:11, 4 January 2006 (UTC)
thread_title:  are boundary points critical points? 

message: The phrase "macroscopic change" links to this page. I was wondering why that is, since that phrase is never discussed on this page. I found the link to macroscopic change on the page for "delta". A derivative is an infintesimal change, which seems to me would also be the meaning of "microscopic change", which links to the page "differential". Does anyone know if a differential is the same thing as a derivative? or what the difference is? Also, what is a macroscopic change? is it an average change? Fresheneesz 22:11, 10 February 2006 (UTC)
thread_title: Macroscopic change

message: "We can write the derivative of f at the point a in two different ways:
:\frac{d\left(f(x)\right)}{dx}\left.{\!\!\frac{}{}}\right|_{x=a} = \left(\frac{d\left(f(x)\right)}{dx}\right)(a)."
I've never seen the second notation ever before ever (probably because it looks like you're multiplying by a... horrible notation). Sorry if that is redundant, but i've *always* *always* *always* seen the notation  f'(a) \!\  or  \frac{df(a)}{dx} \!\  to denote the derivative at the point a. Should I add this? Fresheneesz 01:12, 11 February 2006 (UTC)
thread_title: Denoting the derivative at a point

message: The page heat equation links to this page when talking about a "spatial derivative". there is no article on spatial derivative, and I think some mention of whatever a "spatial derivative" is would be nice to User: fresheneesz
: The heat equation is u_t=u_{xx}. The t variable is called the time variable, and the x variable is the spatial variable. So there is nothing special about it. If anything, it needs to be clarified in the heat equation article. Oleg Alexandrov (talk) 01:34, 16 February 2006 (UTC)
thread_title: Spatial Derivative

message: All in all the derivative article is a very solid piece of work, but it baffles me that it's not mentioned with a single sentence how important this field of mathematics has become in financial analysis/prediction as well as statistical analysis/prediction.
Yes, physics is the most useful field. But it still baffles me I must admit.
Inflection points of a graph can, and is often used, to predict a change in growth of a phenomena. Be it CO2 emission, world population, average temperature change, stocks on exchanges, and much more.
Also, I feel that this article does not show to the reader clearly enough how derivative is used for graph analysis in general.
(I refer to http://www.clas.ucsb.edu/staff/lee/Inflection%20Points.htm for reference)
The--dud 12:48, 25 February 2006 (UTC)
thread_title:  Finding inflection points where f'{{'}}(x) equals zero 

message: My revert was not quite well explained. Of course using symmetric difference will make for a higher order accuracy, so O(h^2) instead of O(h). However, you cannot use the symmetric difference as a definition, as then the absolute value would be differentiable at zero, and it is not. 
Anyways, I found that addition not so helpful, and removed it. Oleg Alexandrov (talk) 18:59, 19 May 2006 (UTC)
replies: text: I really don't think that information belongs right in the section where the derivative is defined. It is distracting and too offtopic, I think. That information should be better off somwhere at finite difference, I'd think. Oleg Alexandrov (talk) 22:37, 19 May 2006 (UTC)

text: I am not sure how important is to discuss in that numerical differentiation article whether derivatives exist. That one is a numerical articles, so you assume things are as nice as necessary. In short, finite difference scheme belong in numerical articles, and existence of derivatives belong into articles like derivative. You are attempting to put in numerical derivatives in this derivative article, and theoretical isssues in the numerical article. I think it is better to keep things compartimetalized. More information is sometimes more confusing, not more illuminating, I would say. :) Oleg Alexandrov (talk) 00:29, 23 May 2006 (UTC)
thread_title:  Symmetric difference 

message: The article gave the pronunciation as "dy by dx", expecting readers to know that "dy" would be pronounced as individual letters and "by" would be pronounced as a word. Does anybody read this stuff? Anyway, my request is that someone who knows how write it out phonetically. I think it might be something like /di waɪ baɪ di ɛks/, based on the IPA chart for English. --KSmrqT 23:43, 19 May 2006 (UTC)
thread_title:  Pronunciation 

message: I think that a few more things should be added could be added the on the rules of differentiation. For instance: \frac{d \log_b x}{dx}=\frac{1}{x\ln b} And other formulas for the differentiation of various kinds of functions. (Trigonometric, exponential, natural exponential, multi-dimensional, etc.) Or perhaps a new article should be created specifically listing such techniques.He Who Is 23:00, 3 June 2006 (UTC)
replies: text: I think a new aricle would be nice to have. These techinques would take too much room in the already big derivative article. Anybody willing to make the techniques for differentiation turn blue? Oleg Alexandrov (talk) 00:40, 4 June 2006 (UTC)

text: Differentiation is not a proper noun, and Wikipedia naming conventions dictate lowercase, so please apply your OCD in compliance with guidelines, instead of in contravention of them. -lethe talk [ +] 02:30, 4 June 2006 (UTC)
replies: text:  Yes, apply your ocd in compliance ... Oleg Alexandrov (talk) 03:29, 4 June 2006 (UTC)
thread_title:  Techniques 

message: I think it might be insightful to include a few sentances about historical objections to the derivation of derivates. I remember reading somewhere some sort of clergyman-mathematician objected to the cancelation of terms that were going to be taken to zero in the x^2 example. This could be followed my a mention that the rigourous treatment provided by analysis solves quells any worries. 131.111.8.99 13:14, 8 June 2006 (UTC)
replies: text: You're surely speaking of the Analyst by George Berkeley. -lethe talk [ +] 13:24, 8 June 2006 (UTC)
thread_title:  Objections 

message: A sentence states the following:
:"For example, if an object's position on a line is given by"
which is followed by a non-linear function. Shouldn't the sentence read, "For example, if an object's position on a curve or parabola"? Or a linear equation could be used as the example? Excuse me if it's a dumb question, as I'm just a first-semester Physics major!
--Dialecticas 17:43, 31 August 2006 (UTC)
thread_title:  Small correction to Physics section? 

message: Derivative of one variable with respect to another when both are functions of other variables: Let x = f(u,v) and y = g(u,v). Now dy / dx = ??.
if u & v are independent, then {(x,y)} is not a function. dy/dx is not defined. If u & v are interdependent, then dy/dx is defined. Jackzhp 23:01, 23 September 2006 (UTC)
thread_title:  About chain rule