Talk:List of differentiation identities

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Derivative of arcoth in this page seems to be wrong.

It think this should be right derivative: [] —Preceding unsigned comment added by 217.159.146.71 (talk • contribs) 18:05, 19 October 2005 (UTC)

lim $$1-cos2xx$$ x→0 —Preceding unsigned comment added by 115.69.140.79 (talk) 07:09, 24 November 2010 (UTC)
 * Corrected. Eric119 04:38, 20 October 2005 (UTC)

Constant Multiple Rule
Thw "Constant Multiple Rule" Seems to be directly consequential of the Chain Rule, so I'll remove it. Anyone with objections, feel free to revert. He Who Is 01:17, 6 June 2006 (UTC)


 * Yes, you can get it quickly from the Chain Rule, but I think it's best to keep it because it's a common occurrence. Also, I don't think any treatment of differentiation would first prove the Chain Rule and then prove this rule. Finally, this rule is part of the statement that differentiation is linear. I'm going to put the rule back in, but under the "Linearity" heading instead of its own. Eric119 23:01, 6 June 2006 (UTC)

Improvement
Woudnt it be more appropriate to say that the derivative of cos a(x) = -a sin a(x), rather than just cos(x) = -sin(x)? --DragonFly31

Why is that an improvement? Eric119 18:34, 14 July 2006 (UTC)

Because it shows the differentiation associated with the constant and sin, not only sin. --DragonFly31 08:00, 18 July 2006 (UTC)


 * I think it is more something like: d(cos a(x))/dx = - d(a(x))/dx . sin a(x). But you are right DragonFly31, it's better than considering the parameter of the cosine function as a constant, which is just a particular case.JeDi 08:16, 18 July 2006 (UTC)

There seems to be some disagreement amoung editors whether including general cases or simple cases is preferrable. Some people seem to prefer putting the simplest case (cos(x) -> -sin(x)) only, and assuming that the more complex cases (like a constant) are a simple application of the chain rule to these basic formulas. Personally, I would prefer that the page contain all common generalizations (like cos(ax) -> -a sin(x)) since many people using this page will be looking for a quick reference and may not remember the chain rule. I took calculus years ago and I was looking up how to differentiate a particular function, which fit this format. I figured it out, but as a reference I would say saving me this extra step (looking up the chain rule and applying it) is useful. People who use calculus on a daily basis may find it redundant, but you probably aren't the audience for a table of simple derivatives. Gruther4 00:47, 24 October 2006 (UTC)


 * I totally agree with Grunther4. I think we should put all of the common functions up like e^(ax) -> a e^(ax), cos(ax) -> -a sin(x), and a^x -> ln(a) a^x. This is a table where you're supposed to be able to look up derivates quickly, not deduce them from each other.

Agreed! This page gives you false formulae given that it takes the appereance of a quick reference page. —Preceding unsigned comment added by 84.238.66.13 (talk) 12:37, 23 September 2008 (UTC)

Please make the formulæ general by including prefixes!

$$(f \circ g)'(x) = (f(g(x)))' = f'(g(x)) g'(x)$$
(see Chain rule) Should we add that to the main table of derivatives? For now we've got only $$(f \circ g)' = (f' \circ g) g',$$ which does not seem to be similar to the formula above. Chortos-2 11:10, 23 October 2006 (UTC)


 * The two formulas say the same thing with different notation. Note that $$f'(g(x)) = (f' \circ g)(x)$$, by definition. Eric119

In derivatives of exponential and logarithmic functions, it says d/dx ln(x) = 1/x. This is wrong. It should be d/dx ln(abs(x)) = 1/x Could someone please change it. I don't know how to write Wikipedia math. —Preceding unsigned comment added by 130.243.97.100 (talk • contribs) 18:09, 12 November 2006 (UTC)
 * Neither statement is incorrect. However, the statement with the absolute value applies to all nonzero real numbers, while the one in the article applies only to positive real numbers. The generalization is easy: just note that d/dx ln(-x) = 1/x for x < 0. I'm dubious as to the value of including ln |x|. Does such a form occur often in any applications? Eric119 01:18, 13 November 2006 (UTC)
 * Then it should say x>0, just as it says c>0 in d/dx logc(x). Otherwise it might get confusing when people try to integrate 1/x and it might lead them to believe it's ln(x) instead of ln|x|. My textbook in math says d/dx ln|x| = 1/x
 * I'm going to bring in d/dx ln|x| = 1/x just below d/dx ln x if noone has a problem with that?

It depends who is the audience. If we are creating reference information for mathematicians then a more geeneral format is advvisable. If we are targeting students then you might want simple forms. —Preceding unsigned comment added by Dumisa (talk • contribs) 12:12, 25 September 2008 (UTC)

Proposed Merge
Seems to be that Techniques for differentiation contains a subset of the content that this page does, and the two combined make for something fairly redundant.Noodle snacks (talk) 11:08, 16 April 2008 (UTC)


 * I think it probably should, too. And besides, there isn't much "technique" to differentiation other than those already shown on other pages and Techniques for differentiation doesn't differ much from the table except that it contains more explanations. --Bobianite (talk) 00:52, 17 April 2008 (UTC)
 * Against. I prefer the table w/o the explanations. I found it very helpful when I had to deal with lengthy differentiation problems. I take a quick look and I find the formula I need. If we flood the article with text and explanations, it will become much more difficult to use. Logain2006 (talk) 15:45, 24 June 2008 (UTC)
 * Against. For the same reasons as above (it would become to cluttered if explanations were added) --Fintelia (talk) 00:20, 25 October 2010 (UTC)


 * There are complicated techniques of differentiation related to differentiation of functions of multiple variables, dirfferentiation in certain direction, differentiation of function defined indirectly etc. Unfortunately no article covers them.--Dojarca (talk) 16:07, 25 September 2008 (UTC)
 * Yeah. Let's merge. This is and always will be duplicate information. dm yers t urnbull   ⇒ talk 20:26, 21 April 2010 (UTC)


 * Seems a good Idea to merge it. The example problems could also be removed and in place of it maybe more generalised examples can be substituted —Preceding unsigned comment added by Souravmishra26 (talk • contribs) 21:47, 22 June 2010 (UTC)

the derivative of an integral
The derivative of an integral should be included. 76.69.254.51 (talk) 01:27, 23 December 2008 (UTC)

proofs
Should proofs be included? I've got pdfs that I've worked out over the years and would be happy to provide. —Preceding unsigned comment added by 24.99.238.85 (talk) 02:18, 7 April 2009 (UTC)

Differentiation of the tetration tower
Hello guys, I propose we include this formula into this section.
 * $$ \frac{\partial^{n}x}{\partial x}=x^{\sum_{i=0}^{n-1}{}^{i}x-1}\ln^{n-1}x+\sum_{i=0}^{n-2}x^{\sum_{i=0}^{n-1}{}^{i}x-1}\ln^{n-2-i}x $$

It should be included because tetration is the next operation in the sequence: addition, multiplication, exponentiation. The derivative for the first three operations are all listed, why not the fourth one?

The proof is given in this document: http://the-genius-group-from-uc-berkeley.googlegroups.com/web/Tetration+Differentiation.pdf?gda=6aA6-FAAAABSYOl_jrsF0EsfPlz6r_UHme_1TQtU2s7OrsZ-qmqDmy7Bkztxd_iq36Pd9mTrcVLHCtiTK2Zr7UgM-Mu5crp8bcVT3VtYGKLco-_l-8AzjQ

I know some of you may say this is "original research." But a mathematical fact is a fact regardless of who did the research, right?

Preceding unsigned comment added by 99.38.249.252 (talk) 09:57, 14 December 2010 (UTC)