Talk:Partial derivative

message: Thanks to all the writers of this page! Saved my behind (-:
Thanks again,
Sam Krupa
Agreed. I've never known what a partial derivate is so I decieded to check it up. Clearly and well written.
---  —Preceding unsigned comment added by 88.114.90.71 (talk) 09:43, 18 March 2009 (UTC)
thread_title: Thanks!!!

message: Since there is only one variable in the formula for the area of a circle, as the article mentions, isn't the example using it a bad one? (Unsigned comment by 68.78.139.53 on 17 May 2006)
:Although it's been many, many years since I've done any maths, I would agree - this example does seem pointless. --A bit iffy 09:54, 11 June 2006 (UTC)
replies: text: I agree. I've removed it. --Spoon! 02:22, 11 September 2006 (UTC)
thread_title: Partial derivative of Area of a circle

message: The third and the fourth paragraph, that is the discussion about the total derivative and the Jacobian are way out of place. Those things are inserted in the middle of the discussion about the partial derivatives, and that is inappropriate.
All that stuff needs to go in the last section, where the gradient is discussed. Other opinions? Oleg Alexandrov 02:27, 23 Mar 2005 (UTC)
thread_title: Disagree with recent changes

message: I'd like to see a section addressing the semantic difference between ∂ and d. For example, if y is only a function of x, then what is the difference between ∂y/∂x and dy/dx. Also, in sloppy engineering notation I've seen dy appear alone; I think I've seen ∂y alone as well. This may be rigerous use of Infinitesimals or it may be engineering shorthand; I'm not sure. —BenFrantzDale 02:00, 5 December 2005 (UTC)
replies: text: I would agree with such a section, but preferably at the bottom of the article; otherwise I would think that it may confuse more than illuminate. Some connections with the Leibniz notation may be made. Oleg Alexandrov (talk) 02:59, 5 December 2005 (UTC)
replies: text:  Now I see, the page I needed to look at was total derivative. —BenFrantzDale 17:40, 15 December 2005 (UTC)

text: What actually is the difference between dy/dx and δy/δx?  Is it just preference? My 2 Cents' Worth (talk) 10:44, 3 June 2010 (UTC)
replies: text:  δy/δx can denote a functional derivative. —wing gundam 03:17, 23 October 2019 (UTC)
thread_title:  Comparison with "''d''" notation 

message: I am a bit perplexed as to why the formal definition is at the end and the example is at the beginning, I think some reordering is in order here! Retardo 22:13, 5 May 2006 (UTC)
thread_title:  Ordering of the sections 

message: In computational mechanics, it is common to denote the surface of a volume as S=∂V. My sense is that this has some underlying meaning in differential geometry. Is it just a notational convenience or is there some rigerous extension of partial differentiation onto volumes? Also, how does this relate to the dV you find in a volume integral? (There dV basically means "one tiny point in V" whereas ∂V basically means "one thin sliver of the surface"; does this relate to the difference between ∂ and d?) —Ben FrantzDale 23:29, 18 May 2006 (UTC)
replies: text: In topology, ∂S denotes the boundary of a surface S.  As far as I know, this is unrelated to the symbol's use to denote a partial differential (I've only just started seeing this formally, so I may be wrong).  I also read this on an article here on Wikipedia which was about the different uses of the symbol; an article that I can't seem to locate now.  If anyone can find it, I'd like to know.  Anyway, I think this makes sense since the boundary of a volume is a surface, as the boundary of an area is a path (at least intuitively).  Hope this helps. Commander Nemet 23:25, 31 May 2006 (UTC)
thread_title:  Surfaces? 

message: It seems that 68.103.26.177 has changed the introduction to say the symbol is from the Greek instead of Cyrillic alphabet. I'm trying not to be hasty and call it vandalism, but unless there is some deeper meaning I am unaware of, the partial differential symbol looks a heck of a lot more like the cursive de (Cyrillic) than a Greek delta.  Furthermore, the intro now purports to say that the Greek letter in question is actually a "d"—something that doesn't exist in that alphabet. Commander Nemet 23:25, 31 May 2006 (UTC)
replies: text: According to Cajori's History of Methematical Notations v. 2, p. 220 Leibniz used a 'δ' for the partial derivative. Thomasmeeks 17:31, 11 December 2006 (UTC)
thread_title: Greek or Cyrillic?

message: Many other mathematics-related articles have an implementation of the topic in various programming languages. Will anybody set up this page with such an example? -- kanzure 16:41, 19 July 2006 (UTC)
thread_title:  Can we get a computerized notation set up? 

message: Is there a WP policy that discourages arguments based on the number of Google 'hits'?  If not, can someone please propose one?
Here for example:
From searching Google today:
* "partial derivative" American ~54000
* "partial derivative" English  ~36400
* "partial derivative" French   ~24000
* "partial derivative" Greek    ~12300
* "partial derivative" Cyrillic ~519
On this basis we'd conclude that: Americans invented partial derivatives, and they probably spoke (a form of) English;  their invention was aided by the French and quickly adopted by the Greek;  and Russians generally know nothing about partial derivatives.
But let's also search >"partial derivative" Amrica<.  It returns ~35800 'hits'.
At least, Google claims that number of hits.  It can't be verified.  Disagree?  Okay, then tell me what hit number 10000 is.
And what about other search engines???
—DIV (128.250.204.118 01:34, 15 November 2007 (UTC)
thread_title:  Number of Google 'hits' inadmissable 

message: Deletion from the previous Edit of the article of:
:'∂' also corresponds to the small Greek delta 'ό' which was also used before the 20th century as partial derivative notation.  
The problem is that that sentence follows a related parenthetical comment.  In retrospect (I introduced the second sentence), if the sentence is going to be included at all, there is a case that both should be parenthetical (to avoid breaking the substanive exposition) or neither (possibly as a footnote or short separate section on the origin of the notation).  Thomasmeeks 14:56, 29 November 2006 (UTC)
thread_title:  Deletion of 2nd sentence of 2nd paragraph

message: "a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary"
the total derivative is, in fact, the sum of the partial derivatives. i seem to remember explaining this before. but no matter. keep removing other people's contributions if you dont understand them  —Preceding unsigned comment added by 212.159.75.167 (talk) 20:26, 13 October 2007 (UTC)
thread_title:  a step backwards

message: We should also discuss the numericalization in this article. At least illustrate how to numericalize the 2nd derivative. anyone agree? Jackzhp (talk) 15:22, 3 May 2008 (UTC)
thread_title: numericalization

message: Hi, i'm currently studying on this topic(partial derivative)  and i need some help to solve these problems.
1. The variable x and r are defined as
	x = r cos θ    and    y = r sin θ.
a)	Explain what is meant by  i)( ∂y/∂r)θ    and  ii)( ∂y/∂r)x   .
b)	Determine the values of (i).
c)	Determine value of (ii) by eliminating θ in the expressions for x and y.
d)	Determine the value of (ii) by the method of function of a function.
e)	Determine the value of :( ∂y/∂r)θ .( ∂y/∂r)x  using method of b) and c).
2.  If  u = ax +by and v = bx – ay, determine the value of:
                (∂u/∂x)y.( ∂x/∂u)v
                                 
3.  A, B and C are the angles of a triangle and u is a function defined as
 
                      u =  sin A sin B sin C.
i)	Express u in terms of A and B only.
ii)	Prove that u is a maximum if the triangle is equilateral.
4.  A vessel to be constructed is in the shape of a cylinder of radius r with equal conical ends, the semi-vertical angle of each cone being α.  If V is the volume and S is the total surface area, show that
             S = 2V/r  + 2πr²(cosecα  - 2/3cotα )
If both r and α can vary, show that for a vessel of fixed volume and minimum surface area, cos α = 2/3, and determine r in terms of V.
Is there anyone able to enlighten me on this problems?
THANKS a million...  —Preceding unsigned comment added by Xpsky (talk • contribs) 05:35, 2 February 2009 (UTC)
replies: text: Please ask this question at Wikipedia:Reference desk/Mathematics. You will most certainly get a response, if you further add your input to the answering of these questions. In general, the talk page is not the most appropriate place to post questions. Further, the problems you quote are rather simple in nature, and similar worked examples can be found in a basic textbook on multivariable calculus. --PST 04:38, 22 May 2009 (UTC)
thread_title:  Need Help 

message: Considering total derivatives article, I feel that the equations should be 
:\frac{\operatorname dV}{\operatorname dr} = \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r} + \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h}\frac{dh}{dr}
:\frac{\operatorname dV}{\operatorname dh} = \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h} + \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r}\frac{dr}{dh}
:k = \frac{h}{r} = \frac{dh}{dr}
instead of 
:\frac{\operatorname dV}{\operatorname dr} = \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r} + \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h}\frac{\partial h}{\partial r}
:\frac{\operatorname dV}{\operatorname dh} = \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h} + \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r}\frac{\partial r}{\partial h}
:k = \frac{h}{r} = \frac{\partial h}{\partial r}
Please verify this.  —Preceding unsigned comment added by Landroni (talk • contribs) 15:00, 18 February 2009 (UTC)
replies: text: Yes, you're right. I have corrected it, and removed the attention box. RupertMillard (Talk) 10:04, 25 February 2009 (UTC)
thread_title:  verify total derivatives 

message: The Introduction chapter mentions "to find the tangent line of the above function at (1, 1, 3)", as well as other instances of "(1, 1, 3)". But the function in question is f(x,y), which takes only two arguments. Its solution at (1, 1) is 3, though, as well as ƒ(1, 1) = 3.  Perhaps it is an error that has slipped by?
:The question above was first posed by User:82.130.38.44, on 23:35, 19 April 2009 (UTC)
replies: text: As 82.130.38.44 determined, ƒ(1, 1) = 3, so (1,1,3) are the (x,y,z) coordinates of a point on the surface. This is a good habit, as some functions will have multiple values of z for some x&y, in which case the derivatives at these different points will most probably be different. RupertMillard (Talk) 09:57, 20 April 2009 (UTC)
replies: text: Of course (1,1,3) is the point on the surface, but is it really a good way of phrasing things?  You wouldn't talk of the derivative of the exponential function e^x at the point (1, e).  Including the value as additional variable does not make any reasonable sense in my silly example, and I am not sure it does in this article (especially without a warning – for me it is just confusing).  Also I don't agree with your point that some functions have multiple values at (x, y).  For me they are just not functions in that case.  You probably think about surfaces defined by an implicit equation, and that can be described by several "charts", involving several functions. --Bdmy (talk) 10:25, 20 April 2009 (UTC)
thread_title:  Three arguments to a two-variable function? 

message: This article discusses intuition but fails to discuss the main properties of the partial derivative; only at the end is the formal definition stated. For example, many facts found in a basic calculus textbook are not discussed, regarding the partial derivatives. What worries me, is that even the content of a basic calculus textbook is not adequate enough for this concept. --PST 04:35, 22 May 2009 (UTC)
thread_title:  This article needs work 

message: Doesn't f sub x = the partial of f / the partial of x? (not the partial of f / the partial of y)
see basic definition, where f sub a takes y to be the variable.
: No, that's not what it means in that case.  Read the defitions given just before that.  The subscript doesn't represent any sort of derivative at all.  That conflicts with the notation used elsewhere in the article, so that's potentially confusing.  But the paragraph preceding that part is explicit about what the notation means. Michael Hardy (talk) 22:36, 20 September 2009 (UTC)
thread_title:  Question 

message: My compliments to whoever has guided this wiki page, be it a group or an individual.
The introduction is EXCELLENT!  — Preceding unsigned comment added by 220.165.68.56 (talk) 07:13, 8 January 2013 (UTC)
thread_title:  Good Job!! 

message: In the Notation-section it says:
:\frac{\partial^2 f}{\partial y \, \partial x} = ... = f_{xy}
But in the Higher order partial derivatives-section it says:
:\frac \equiv ... \equiv f_
So my basic question is the meaning of \frac{\partial^2 f}{\partial x \, \partial y}:
# Does it mean, that you first differentiate with respect to x and then with respect to y, because that is the order of the denominator?
# Or does it mean, that you first differentiate with respect to y and then with respect to x, because derivative operators always work on the stuff, that comes after it? (So basically read from right to left, rather from left to right?) 134.60.31.73 (talk) 16:27, 10 April 2015 (UTC)
replies: text: The theorem on symmetry of second derivatives says that the two are equal--you get the same thing regardless of the order in which you take the derivatives. (This is mentioned at the end of the subsection "Formal definition".) So it doesn't matter how you interpret the notation, though it is standard to mean \frac{\partial^2f}{\partial x \partial y} \equiv \partial \left( \frac{\partial f}{\partial x} \right)/ \partial y,  as is implicit in the H matrix in the article Hessian matrix. Loraof (talk) 20:09, 9 May 2015 (UTC)
replies: text:  Thank you for your answer. But in the same article symmetry of second derivatives is says that this symmetry does only hold under special requirements, so it is not generally true, see here []. So in the general case it does matter how I interpret the notation. Also in your mentioned article Hessian matrix I cannot find any passage that supports your mentioned "standard", perhaps you can elaborate? I would have chosen the opposite interpretation (my second alternative from my initial post).134.60.31.73 (talk) 12:06, 19 June 2015 (UTC)
thread_title:  Inconsistency regarding Second-order mixed derivatives 

message: Substituted at 02:27, 5 May 2016 (UTC)
thread_title: Assessment comment

message: I think the red term in the quote
:The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by f^\prime_x,\ {\color{red}{f_x}},\ \partial_x f,\ D_xf,\ D_1f,...
can not be correct, can it? I think that would be the undifferentiated function, not the derivative. --Yukterez (talk) 02:01, 4 September 2017 (UTC)
thread_title:  f´(x)=f(x)? 

message: I recommend that the definition of partial derivative either include a hyperlink to Standard Basis or define e_i. Cahdfin13773 (talk) 00:25, 19 July 2023 (UTC)
thread_title:  Hyperlink to Standard Basis