Talk:Quotient rule

Regarding Limitations

$f(x)={\frac {|x|}{|x|}}$ is not at all differentiable at $x=0$; it's not even defined there. 138.89.101.39 (talk) 00:18, 10 April 2009 (UTC)

Informal proof

Out of curiosity, what exactly is there about the informal proof that makes it informal? Cburnett 23:22, 3 Feb 2005 (UTC)

I guess it's considered an informal proof because it's based off the product rule, while the "formal" proof is based off the difference quotient, which is more direct. I changed the headings to be more specific. - Evil saltine 05:11, 4 Feb 2005 (UTC)

This was proofed by Sir Al-Hinai Quotient, who was regarded as the leader of classical mathematics- at his time. —Preceding unsigned comment added by 128.243.220.21 (talk) 02:11, 18 May 2009 (UTC)

The proof is informal because it contains a hidden assumption, that the derivative of f exists. David Radcliffe 02:44, 26 May 2007 (UTC)

Total differential proof

The total differential proof uses the fact that the derivative of 1/x is −1/x². But without the quotient rule, one doesn't know the derivative of 1/x, without doing it directly, and once you add that to the proof, it doesn't seem as "elegant" anymore, but without it, it seems circular. Revolver 16:03, 30 September 2005 (UTC)

I would vote to remove that proof altogether. Too many proofs in this article, and they are lengthy and using lots of calculations. Oleg Alexandrov 17:44, 2 October 2005 (UTC)

I guess I'll go ahead and get rid of it. I'll save the section incase anyone wants it back. (Frazz 18:04, 7 February 2007 (UTC))

On second thought, it's fine really. (Frazz 16

30, 8 February 2007 (UTC))

This total differential proof uses knowledge of what the derivative of 1/x is. If you know that, you can prove the quotient rule in two lines using the product and chain rules, not having to go through a huge mumbo-jumbo of differentials. I really don't know why such a proof is not on this page and numerous complicated ones are. 67.149.103.91 (talk) 04:24, 17 June 2010 (UTC)

Fix needed in a proof

A proof of the quotient rule is not complete. Why $h(x)$≠ 0 does implies $h(x+\Delta x)\neq 0$? I have seen a proof of the quotient rule based on a characterization theorem (don't know its proper English name). --Matikkapoika 01:25, 15 November 2006 (UTC)

I know I'm no expert and am probably spouting rubbish, but would it be that $h(x)\neq 0\Rightarrow h(x+\Delta x)\neq 0$ as $\Delta x\to 0$, i.e. $h(x+\Delta x)\to h(x)\neq 0$? 118.90.51.62 (talk) 02:13, 22 June 2008 (UTC)

From the product rule

The text:

The rest is simple algebra to make f'(x) the only term on the left hand side of the equation and to remove f(x) from the right side of the equation.

on my PC, I can't see the dash after the f

SethMould 07:53, 16 July 2007 (UTC)

Mnemonic Section

A simple mnemonic can be used to recall the quotient rule when solving derivatives by hand: "lo Dhi, minus hi dlo, cross the line and square below"

Extra '('

There is an extra open brackets in the third line of the first proof. —Preceding unsigned comment added by 201.95.65.32 (talk) 17:47, 15 December 2009 (UTC)

From the Product Rule

As noted above, the simplest proof is from the product rule. A proof from the product rule used to be part of the article, and since it helps in memorizing the rule, I don't see why this short proof is not in the article.

The following text works:

The shortest proof comes from the product rule. It is not hard to prove by various means that ${\frac {d}{dx}}\left({\frac {1}{x}}\right)=\left({\frac {-1}{x^{2}}}\right)$. For a short proof of this fact, note that $x^{-1}=e^{-\ln(x)}$ and apply the chain rule. Another direct application of the chain rule tells us that ${\frac {d}{dx}}\left({\frac {1}{g}}\right)={\frac {-g'}{g^{2}}}$. The quotient rule then follows:

${\frac {d}{dx}}\left({\frac {f}{g}}\right)={\frac {d}{dx}}\left(f\cdot {\frac {1}{g}}\right)=f'\cdot {\frac {1}{g}}-f\cdot {\frac {g'}{g^{2}}}={\frac {f'g-fg'}{g^{2}}}$

Mistake

The very first definition of quotient rule is wrong. There is mistake of sign. — Preceding unsigned comment added by 184.17.73.223 (talk) 23:16, 15 January 2012 (UTC)

Mistake

The second derivative was incorrect. Denominator should be to the power of 3 to make numerator consistent with maths and h-prime term in the numerators 3rd term should have been squared. From formating these look like purely clerical errors. Double checked with maple13. — Preceding unsigned comment added by 94.195.250.134 (talk) 19:58, 25 March 2012 (UTC)

I agree. I added a fact tag for now. Rlendog (talk) 00:18, 21 December 2018 (UTC)

Jumps between g(x) an j(x) or equivalents in successive rendered(TeX) examples.

In the introducing article, jumps occur between g and j functions every other rendered example (once j then g then j ...); they appear to be the same. I don't have the expertise to affirm it is wrong in the current form.

In the Proof>Algebraic_Proof section, the jump occurs following the introduction of f'(x) as the question that is to be answered. j(x) and h(x) are used as the functions comprising f(x) when they're divided. Taking 1/delta x as a factor and combining the two remaining fractions shouldn't (algebraically) affect j(x) in any way contrary to what's demonstrated. In this case, g(x) is substituted for j(x) for no apparent reason.

My observations may not be accurate so I need either a confirmation or a clarification. In case of the earlier response, I'll rewrite the TeX code. — Preceding unsigned comment added by Enamex (talk • contribs) 17:28, 24 September 2012 (UTC)

Derivation (The Uncomplicated One)

I couldn't help noticing that the Quotient Rule article is a stub. Here's a possible proof that doesn't fall into the same pithole that the previous proof fell through.

Let some function $f(x)={\frac {g(x)}{h(x)}}$.

We wish to find ${\frac {d}{dx}}f(x)$, and this is equivalent to ${\frac {d}{dx}}{\frac {g(x)}{h(x)}}$.

We also know that $g(x)=f(x)*h(x)$.

By the product rule, we can say that ${\frac {d}{dx}}g(x)=h(x)*{\frac {df(x)}{dx}}+{\frac {dh(x)}{dx}}*f(x)$.

From the equation above, ${\frac {d}{dx}}f(x)={\frac {{\frac {dg(x)}{dx}}-{\frac {dh(x)}{dx}}*f(x)}{h(x)}}$

Because $f(x)={\frac {g(x)}{h(x)}}$, the right side simplifies to ${\frac {{\frac {dg(x)}{dx}}-{\frac {dh(x)}{dx}}*{\frac {g(x)}{h(x)}}}{h(x)}}$, which simplifies to ${\frac {d}{dx}}f(x)={\frac {{\frac {dg(x)}{dx}}*h(x)-{\frac {dh(x)}{dx}}*g(x)}{h^{2}(x)}}$, completing the derivation.

There's another proof stemming from the original definition of the derivative that is also quite simple to understand (and rigorous). The article would benefit by its addition. Gummygoodness (talk) 04:23, 11 March 2013 (UTC)

At a glance it looks good. My only criticism is that "*" is not normally used for multiplication in maths, in my experience. I think just remove the "*" and have the multiplication implied. Adpete (talk) 11:13, 11 March 2013 (UTC)

Rollback

This article should be rolled back to just before the first edit of July 11, 2016 when someone deleted a big chunk without explaining why and also put in an incorrect formula (the formula was correct before this edit). Jrheller1 (talk) 05:13, 19 August 2016 (UTC)

I added implicit differentation and higher order formulas section (which was the useful information contained in the version before July 11, 2016). So I don't think rolling back would be useful anymore. Jrheller1 (talk) 22:07, 19 August 2016 (UTC)

What happened to this article?

Looking back several years in the history, this article used to be much better. It had a lot more info and was better written. But somewhere along the line, it seems to have been gutted and remade poorer. I'm working on fixing it up some, and I'll add a todo list in a moment with a couple things I think it needs. --Deacon Vorbis (talk) 16:02, 23 April 2017 (UTC)

one little comma

One of my edits has now been reverted twice. I've put it back once more and started this section to help clear up the issue. The sentence in question (with the comma I added -- the one immediately preceding "and solving for...") is:

Implicit differentiation can be used to compute the nth derivative of a quotient (partially in terms of its first n-1 derivatives). For example, two implicit differentiations of $fh=g$ yields $f''h+2f'h'+fh''=g''$, and solving for $f''$ yields

$f''=\left({\frac {g}{h}}\right)''={\frac {g''-2f'h'-fh''}{h}}.$

According to any grammar guide I can find (such as point #1 in this guide), a comma is necessary here because we have two independent clauses joined by a coordinating conjunction. Even if one could argue it's not strictly necessary, it would still appear to be preferred with the comma. --Deacon Vorbis (talk) 23:56, 23 April 2017 (UTC)

The following is User:Jrheller1's response, which I've copied here from my talk page in order to keep the discussion in one place:

See section "Comma abuse" (13.) in the grammar reference you cited in an edit summary for quotient rule. Rule 1 is for independent clauses. The two sequential steps in a simple mathematical procedure are not independent. The sentence in the quotient rule article is structurally the same as "we laid out our music and snacks and began to study" (two sequential steps in a simple procedure).

(signing just for completeness) --Deacon Vorbis (talk) 02:28, 24 April 2017 (UTC)

Rule 1 applies because there are two independent clauses in this sentence -- there are two subjects, each with their own verbs:

• subject 1 is "two implicit differentiations"
• verb 1 is "yields"
• subject 2 is "Solving for $f''$
• verb 2 is "yields"

Rule 13 doesn't apply because this is not a compound predicate. An equivalent everyday example would be something like "Alice ran to the bakery, and Bob ran to the cafe". The example you gave isn't equivalent because it only has one subject ("We").

Also, again, please undo your latest revert, as it's in violation of WP:3RR. --Deacon Vorbis (talk) 02:40, 24 April 2017 (UTC)

I made the wording less awkward in that sentence. Hopefully that will resolve this issue. Jrheller1 (talk) 03:04, 24 April 2017 (UTC)

Which changes are not helpful?

@Deacon Vorbis: On the examples and proofs:

1. I've been trying to keep a long equation separate from long wording, so I have been breaking them up in an effort to improve readability.
2. I usually see a fraction to the left of a long equation (such as for a limit, derivative, or integral, as examples) that it is factored out of, so I have been trying to do that.
3. (I understand that the last equation in a section, etc, should have a period at the end of it, so I have left periods there after the first time they got reverted.)

Could you please tell me which changes you are not finding helpful, and why?
Thank you - I appreciate the cooperation. -- Bwefler (talk) 15:58, 1 February 2018 (UTC)

Formulas can certainly be set apart from text, but they should usually be by themselves, not with other running text, and on Wikipedia, the standard is to do so by indenting with a : (although there's some talk about this changing, but that doesn't really matter for now). Throwing in a bunch of scattered <br>s is certainly not the way to do it. However, a simple statement of the product rule isn't an especially long or complex formula, and setting too many apart tends to break up the flow of the text. As for the fraction, it was originally separated on the right hand side, so it's probably good to leave it there. It could have just as easily been taken out on the left also, but multiplication is commutative, and it's fine either way – there's no particular good reason to change it. –Deacon Vorbis (carbon • videos) 16:21, 1 February 2018 (UTC)

Acknowledged. -- Bwefler (talk) 16:33, 1 February 2018 (UTC)

Higher Order Formulas

The higher order formula seems incorrect. At a minimum, the denominator should be h^3, and even with the g/h terms in the numerator that would only get to h^2. I am not quite getting the same numerator either, but I may have made an error or there may be another algebraic step needed. For now I added a citation needed tag, but if this can't be supported by a reliable source or by showing more intermediate steps it needs to be removed. Rlendog (talk) 00:21, 21 December 2018 (UTC)

@Rlendog: What's there is correct. If you expand out the $f'=(g/h)'$ term in the rightmost expression, it will be as you're expecting. I'm inclined to remove the {{cn}} tag per WP:CALC. –Deacon Vorbis (carbon • videos) 00:49, 21 December 2018 (UTC)

I don't think that's obvious from the formulas shown. I am ok with removing the tag without an explicit source, but then the intermediate formulas need to be shown. Rlendog (talk) 17:36, 21 December 2018 (UTC)

Well, I added in one extra step (I think it was there at some point in the past but got removed somewhere along the way). I'm not sure if that's what you're referring to though. Earlier I also removed the plain $f=g/h$ substitution at the end as not really necessary. As it stands now, it gives an expression for $f''$ partially in terms of its lower derivatives, as advertised. Someone could always sub in more, but I'm not sure how illuminating that would be. –Deacon Vorbis (carbon • videos) 19:03, 21 December 2018 (UTC)

Avoiding comma abuse in a statement of two sequential steps

The statement "Differentiating fh=g twice and then solving for the second derivative of f" has exactly the same structure as "We laid out our music and snacks and then began to study". The result of the differentiation should be given as a parenthetical statement. Jrheller1 (talk) 17:28, 8 March 2019 (UTC)

A sentence describing the two steps of a single mathematical procedure should not be composed of two independent clauses. If it appears that the two steps are independent clauses, then the sentence should be rewritten so that it is clear they are not independent clauses. This is exactly what I did with my edit. I will be reverting back to my last edit if there are no objections on the talk page. Jrheller1 (talk) 17:06, 9 March 2019 (UTC)

There is absolutely no reason why you can't break something like this up into two independent clauses. Moreover, what constitutes a "single mathematical procedure" is somewhat arbitrary and subjective. There are two conceptually separate steps here: 1) differentiating, and 2) solving for one term. Looking back over the history, someone else had complained about the terseness, and so I added a step back in as a compromise (not even remembering why it was gone in the first place). Awkwardly forcing it to be a single predicate by placing part inside parentheses isn't appropriate. –Deacon Vorbis (carbon • videos) 17:41, 9 March 2019 (UTC)

I forgot to mention also that your analysis of the sentence structure is completely incorrect. See the older discussion further up the talk page. –Deacon Vorbis (carbon • videos) 17:42, 9 March 2019 (UTC)

I should have used rule 14: "Don't put a comma between the two nouns, noun phrases, or noun clauses in a compound subject or a compound object". "Differentiating fh=g twice and then solving for the second derivative of f" is a compound subject, so "Differentiating fh=g twice, and then solving for the second derivative of f" would be wrong.

My preferred form of this sentence is a compound subject ("Differentiating fh=g twice [with result here] and then solving for the second derivative of f"), a single verb (yields), and a single object (the final equation for the second derivative of f).

Your preferred form is two clauses ("Differentiating fh=g twice yields x" and "solving for the second derivative of f yields y"). Why do you think this form is better? Jrheller1 (talk) 19:39, 9 March 2019 (UTC)

I also don't understand why you insist on placing a comma between the two clauses in your preferred form. For a two-step procedure, "Step 1 yields intermediate result A and then step 2 yields final result B" seems fine to me. Even though there is no subordinating conjunction between the first clause and the second clause, the second clause is obviously dependent on the first clause; and grammar references state that no comma should be used between an independent clause followed by a dependent clause. Of course, commas must be used in a three-step procedure: "Step 1 yields intermediate result A, then step 2 yields intermediate result B, and step 3 yields final result C". Jrheller1 (talk) 21:11, 9 March 2019 (UTC)

This really should settle the issue. The comma doesn't belong in either of the two possible sentence structures. In the two clause structure, the first clause is independent because it can be a sentence by itself. The second clause is dependent because it cannot be a sentence by itself ("solving for the second derivative of f yields y" is meaningless without the first clause). But the compound subject, verb, object structure is better because it doesn't use the verb "yields" twice. So I will be reverting back to my last edit unless someone objects on the talk page. Jrheller1 (talk) 03:11, 10 March 2019 (UTC)

No, this doesn't settle it. It's not currently a compound subject. You could turn it into a compound subject as you indicated, in which case a comma wouldn't be needed, but to do that, you either have to remove the intermediate result (which I put back in ages ago because someone (reasonably) complained about the terseness, as I indicated), or you have to add it in as some sort of parenthetical, which would be awkward. For crissakes, this is getting absolutely ridiculous. Please just drop this already. –Deacon Vorbis (carbon • videos) 03:23, 10 March 2019 (UTC)

My last edit (which you reverted) has the compound subject, verb, object form. In the current two clause form, the comma still shouldn't be there since it is an independent clause followed by a dependent clause. Adding the intermediate result as a parenthetical is not awkward at all. Jrheller1 (talk) 03:30, 10 March 2019 (UTC)

It's two independent clauses joined by a coordinating conjunction (and). Seriously, drop this; it's way past ridiculous at this point. Both our times would be better served doing other things. –Deacon Vorbis (carbon • videos) 03:46, 10 March 2019 (UTC)

As I stated above, the current form is an independent clause followed by a dependent clause, so a comma between them is wrong. You have been attempting to edit war an incorrect comma into text that I originally wrote from April 2017 up to the present. I have no trouble admitting when I am wrong, but in this case, you are definitely wrong, so you are the one who needs to drop this. Jrheller1 (talk) 04:25, 10 March 2019 (UTC)

And you're still wrong; it's two independent clauses separated by a coordinating conjunction. There's nothing more to say about this. –Deacon Vorbis (carbon • videos) 16:34, 10 March 2019 (UTC)

As I have stated multiple times above, the second clause ("solving for the second derivative of f yields y") is meaningless without the first clause, so it is dependent on the first clause. You are clearly wrong and clearly have a problem admitting this. Jrheller1 (talk) 16:39, 10 March 2019 (UTC)

It doesn't matter whether or not it's conceptually meaningful or meaningless. Syntactically, it's independent. Just fucking stop already. –Deacon Vorbis (carbon • videos) 17:04, 10 March 2019 (UTC)

The second clause is obviously dependent on the first. But even if you assume that the second clause is independent, there still should not be a comma between the clauses because this is a list of two items. The sentence "Alice is 8 and Bob is 9" is composed of two independent clauses. But since it is a list of two items (the ages of two individuals), there should be no comma between the clauses. Jrheller1 (talk) 18:34, 10 March 2019 (UTC)

Your behavior here is very disruptive. The reason I removed the intermediate result back in 2017 was to try to get you to stop edit warring the incorrect comma into the text I wrote. My latest edit is an improvement over my text from 2017 since it eliminates the double use of the verb "yields". Jrheller1 (talk) 18:34, 10 March 2019 (UTC)

Before you go throwing stones, the version that was in place had been reached by compromise between myself and another editor. You came in here way later and decided to change it. You were reverted. You attempted to discuss, which is great, but you were unwilling to accept the fact that you didn't convince (even remotely) the only other editor in the discussion (myself) that the change was a good one. The only disruption here was initiated by you. Since you've been unwilling to accept the version that was in place, I've listed this for input at WP:3O. Please refrain from making any further changes until there's been feedback from there. –Deacon Vorbis (carbon • videos) 19:02, 10 March 2019 (UTC)

You're being very dishonest about your behavior here. The "version that was in place" or "compromise between myself and another editor" was simply my text with your incorrect comma added. I wrote two versions of the sentence. Version 1 is the two clauses without the unnecessary comma. Version 2 is the improvement from March 8 with a compound subject, single "yields", and single object. The only thing I'm unwilling to accept is the unnecessary comma that you keep trying to edit war into my text. You have made at least 7 edits forcing this unnecessary comma into my text. If that's not disruptive, I don't know what is. Jrheller1 (talk) 19:33, 10 March 2019 (UTC)

It's not your text. Other people can come in later and modify it. The change I made most recently was in response to another editor's concern about omitted steps. I've backed up my claim about the correctness of a comma with evidence from grammar guides, while you've continued to shift the goalposts about why it's needed. Your latest reasoning about a list of two items doesn't apply because this isn't a list. If that reasoning were valid, you could apply it to any sentence with two independent clauses joined by a coordinating conjunction. Moreover, the example you used does require a comma because it has two independent clauses joined by a coordinating conjunction. You might get away with omitting the comma there because each clause is so short, but that's irrelevant to the case at hand. –Deacon Vorbis (carbon • videos) 20:32, 10 March 2019 (UTC)

You're being intentionally obtuse. I know very well that nobody owns anything on Wikipedia. What I clearly meant was that I wrote the text of the sentence. The only edit you ever made to that sentence was repeatedly adding the incorrect comma. Back when you were edit warring the unnecessary comma into the sentence in April 2017, I removed the "yields $f''h+2f'h'+fh''=g''$" in an attempt to stop you from edit warring the unnecessary comma into the sentence. Sometime between then and December 21, 2018, some other editor corrupted the formula. Then on December 21, 2018, you put back the text I wrote (including the "yields $f''h+2f'h'+fh''=g''$") plus your unnecessary comma.

I'm not "shifting the goalposts". I have always known that the comma was unnecessary. I don't think about grammar rules when I'm writing; it's something that becomes intuitive after a while. You are forcing me to waste time looking for the specific grammar rules showing that the comma is unnecessary. Now I have found them. First rule: no comma between independent clause followed by dependent clause. Second rule: no comma between items in a two-item list. The sentence definitely is a list (more specifically, an ordered list) of two steps in a mathematical procedure. The reason "Alice is 8 and Bob is 9" shouldn't have a comma is precisely because it is a two-item list, not because the clauses are short. "Alice is wealthy, but Bob is poor" definitely requires a comma.

This is such a minor issue that this debate over grammar is really a waste of time. But your behavior is totally responsible for this waste of time. If you (or any other editor) had placed an unnecessary comma somewhere in a sentence you wrote, I probably would not have even bothered to remove it. I definitely would have immediately dropped the issue if my edit was reverted. Jrheller1 (talk) 22:12, 10 March 2019 (UTC)

3O Response: Commas do often come up in punctuation disputes. I also tend to look at this as an inline list which is introduced with For example,. A list with two items does not need a serial comma before the and as might be used with a longer list. However, instead of simple terms, the list items here are independent clauses. (Despite the second clause representing a secondary step in the process being described, it is not grammatically subordinate to the previous clause.) While a comma isn't required as a list separator, I believe that a separator is required for the clauses. From the lede of independent clause is this sentence: Independent clauses can be joined by using a semicolon or by using a comma followed by a coordinating conjunction (and, but, for, or, nor, so, yet, etc.). Thus this could be ; then or , and then. You can find some common examples of an and then construction at wikt:then. Please note that the punctuation introducing the list should be raised from a comma to a colon; there needs to be greater separation between For example and the rest of the sentence than the separation between the clauses. (This would also be consistent with an example near the top of the article.) It might be worthwhile to have an wikicomment following the comma to explain to editors why it is there. This is a non-binding third opinion but I hope that it helps! If you want further clarification, I would recommend asking at Wikipedia:Reference desk/Language or Wikipedia talk:WikiProject Guild of Copy Editors. – Reidgreg (talk) 12:16, 12 March 2019 (UTC)

This doesn't really address the issue. The text I want is: "differentiating $fh=g$ twice (resulting in $f''h+2f'h'+fh''=g''$) and then solving for $f''$ yields final result". The text the other editor wants is: "differentiating $fh=g$ twice yields $f''h+2f'h'+fh''=g'',$ and then solving for $f''$ yields final result". It is obviously better to avoid two uses of the word "yields" in the same sentence. Jrheller1 (talk) 01:01, 21 March 2019 (UTC)

Also: the text I prefer is closer to the stable version (from April 23, 2017 to December 21, 2018) than the text DV prefers. If someone other than DV does not explain why DV's preferred version is better, I will be reverting back to my preferred version. Jrheller1 (talk) 16:21, 21 March 2019 (UTC)

Cause of edit warring over a comma

The thing that bugs me about this is that Deacon Vorbis has been consistently trying to blame me for the edit warring over a comma in this article. See the comment he left on my talk page back in April 2017 and also his comments in the discussion above.

I wrote a sentence. He added an unnecessary comma to the sentence I wrote. Then I reverted his addition of an unnecessary comma. At this point, WP:BRD indicates that the reverted editor should start a discussion if they wish to challenge the revert. But since the issue is so minor, any reasonable editor would have just dropped the issue at this point.

Then he started the edit war by reverting my deletion of his comma without any discussion. The fact is, he is totally responsible for the edit warring over a comma in this article. And he is still insisting that his edit-warred-in version with his unnecessary comma prevail, even though my latest version is definitely an improvement (it gets rid of the double use of the word "yields" in a single sentence).

If and when I revert his latest revert, the purpose will be to get rid of the double use of the word "yields" and also to remove any possible ambiguity over the need for a comma. He has no good reason to object other than wanting to get his way. Jrheller1 (talk) 18:24, 11 March 2019 (UTC)

I don't want to waste the time of any other editors with this silly dispute. What I do want is for Deacon Vorbis to end the edit war by not reverting me when I restore my improvement later this week. Jrheller1 (talk) 00:28, 12 March 2019 (UTC)

Your edits aren't improvements; your use of a comma is incorrect. I've explained this many, many times already. I've pointed you to a grammar guide with very clear reasoning (any other guide will tell you the same thing, so I'm not even cherry picking here). You've just continued to deny reality about this while offering no evidence to support your position. I don't see what else I can say to convince you, but I did ask for a WP:3O, so please stop threatening to continue this stupid edit war and just wait to see what comes out of that. –Deacon Vorbis (carbon • videos) 00:38, 12 March 2019 (UTC)

As I just explained above, you started the edit war, so it is your responsibility to end it by not reverting me. My edit from March 8 that you reverted has a compound subject with two nouns. There is a grammar rule clearly stating that there should not be a comma between the two nouns. Even the current form (comma between the two clauses) has always "looked" wrong to me, and now I have found the grammar rule explaining why: no comma between the items in a two-item list. Jrheller1 (talk) 00:59, 12 March 2019 (UTC)

You agree this is a silly dispute. So why do you want to waste the time of other editors with it? Do you think they will appreciate having their time wasted? Jrheller1 (talk) 00:59, 12 March 2019 (UTC)

It's not a fucking list. A sentence cannot just be a list. It's two independent fucking clauses joined by a coordinating fucking conjunction. As I already pointed out, if your reasoning were valid, then any fucking sentence with two independent fucking clauses joined by a coordinating fucking conjunction would be a list of two items and have the comma omitted. But then there would be no need for the pretty basic rule about having a comma there in the first place. It doesn't matter if it "looks" wrong to you. It matters what people who know what they're talking about advise, and they advise that there should be a comma there. You yourself said you don't pay attention to rules and just go by what feels intuitively right, but your intuition can fail, and it has failed here. Your edit was completely unnecessary; its only purpose was because you have some weird fucking obsession with the fact that it got rephrased back in a way that required the comma, because another editor didn't like the omitted step. You were nowhere to be found when that was going on, and it had been in place for months before you dropped back in to stir this same shit up again. I've said all there is to say – multiple times. I'm done discussing this until someone can step in and offer another view. –Deacon Vorbis (carbon • videos) 01:15, 12 March 2019 (UTC)

I'm not getting involved in the specifics on this, but offer my sympathies and a little advice. I am also a strong proponent of WP:BRD, but note that this is an editing practise and has not gained community consensus as a guideline or policy. Editors are under no requirement to follow BRD. I would also note that in a dispute between two editors, if one is edit warring then by definition they both are. I know that can suck if all you're trying to do is keep the article stable, but sometimes you have to live with what you feel is an "inferior" version of an article until you can reach some form of consensus. Edit warring is disruptive, period, no matter how correct you believe you are, or how much good work you may have done on the article. If you're unable to resolve the dispute on the article talk page and have to go through dispute resolution, it's more work for other editors to go through the diffs and edit warring looks bad for all parties involved. I was claiming BRD while in a dispute with an editor on my first GA, and ended up edit warring which led to the article being put under protection and almost jeopardized its appearance on the main page. Even if I was right, I was going about it the wrong way. Sometimes you have to live with what you may feel is an inferior version of an article while patiently going through discussions or, if it comes to it, months of dispute resolution.

Ideally, disputes can be resolved on the article talk page, which requires less time and effort. Assume good faith, listen and be open-minded, and don't respond adversarially. I feel this is especially important with the little things, like a comma, as few volunteers will spend their time to help resolve deadlocks over such. Try not to take things personally, and if you do get upset then find something else to work on for a while; there's plenty to do on Wikipedia. If you have time, there are a ton of essays at Wikipedia:Essay directory § Wikipedia's code of conduct with advice. – Reidgreg (talk) 12:20, 12 March 2019 (UTC)

This is nuts

@Jrheller1: Please stop. I thought this was settled, and yet you've reignited the edit war. There was even a third opinion generously offered. And I realize it's not binding, but it's the best we've got. The version you've reverted to was not the "stable" one. Please, please, please just let this one go. –Deacon Vorbis (carbon • videos) 19:27, 24 March 2019 (UTC)

Changes in notation that got reverted

I kept on changing $f(x)=g(x)/h(x)$ to $h(x)=f(x)/g(x)$ even though it’s just notation and not an improvement to the article because the latter is commonly used in textbooks and online resources, but it turns out the former has been long established on this page. Sorry for the unnecessary changes. Also, I replaced k with $\Delta x$ in the limits since normally $\Delta x$ or h but not k is used to represent the change that approaches zero in the derivative, but since h was taken for a function, the remaining common choice was $\Delta x$. Please take note though that my other edits also got reverted when only the changes in notation were unnecessary. 49.147.83.13 (talk) 16:49, 21 May 2020 (UTC)

Your other changes were mostly not improvements either. There were already a couple reasonably representative examples in place, we don't need more (similar) ones. Having too many runs afoul of WP:NOTTEXTBOOK. Likewise, additional proofs are pretty unneeded at this point, and probably more importantly, your "proof" using logarithmic differentiation is only even valid when both functions are positive. Also, the section headers don't have to state every bit that goes into them; they just have to serve as a means to help tell themselves apart. On a side note, I find the "reciprocal rule" a silly extra rule that serves no purpose. Most Calculus texts that I've seen don't even bother to name or prove it separately. –Deacon Vorbis (carbon • videos) 17:22, 21 May 2020 (UTC)

Thank you for explaining that you disagree with the logarithmic differentiation proof and find the reciprocal rule quite trivial. 49.147.83.13 (talk) 17:27, 21 May 2020 (UTC)