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: [[1]] —Preceding unsigned comment added by 217.159.146.71 (talk • contribs) 18:05, 19 October 2005 (UTC)

• Corrected. Eric119 04:38, 20 October 2005 (UTC)

Contents 1 Constant Multiple Rule 2 Improvement 3 4 Proposed Merge

[edit] 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)

[edit] 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.

[edit]

(see Chain rule) Should we add that to the main table of derivatives? For now we've got only 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 , 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?

[edit] 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)