Talk:Logarithmic differentiation

Special consideration

The logarithmic differentiation can be used for negative functions as well by using absolute value because

$(\ln |x|)'={\frac {1}{x}}$

In case where the function is zero, log differentiation is not applicable because of a division by zero, however, in the following formula

$f'(x)=f(x)\cdot (\ln |f(x)|)'$

does the right hand side of the equation have a removable discontinuity at a point where $f(x)=0$ and $f'(x)$ exists? Probably not, differentiability does not imply continuous differentiability. (Igny (talk) 16:44, 28 May 2009 (UTC))

Examples

I disagree that a Wikipedia article cant have examples to illustrate the point. So I copied a couple of examples here (Igny (talk) 00:22, 29 May 2009 (UTC))

It doesn't matter if you disagree. Policy disagrees with you. We have the general cases, and having examples starts to verge on being textbook-like – which is for Wikibooks. —Anonymous Dissident^Talk 07:57, 29 May 2009 (UTC)

Could you point me to the link of the relevant policy?(Igny (talk) 13:07, 29 May 2009 (UTC))

And are you saying that differentiation itself violates some WP policy? (Igny (talk) 13:09, 29 May 2009 (UTC))

WP:NOT. This article once had examples; I myself inserted them. Others felt it made it look too textbook-y. I think it's fine without them. I have a question, though: is the section using the capital pi and sigma notation really necessary? It seems to be redundant to the section above it. Furthermore, none of the other sections use capital pi or sigma, when, at the very least, the product section easily could. My personal opinion is that it's not needed. I think it makes the matter more complex than it needs to be. What do you think? —Anonymous Dissident^Talk 23:44, 29 May 2009 (UTC)

No examples, fine by me. Did you see any pi or sigma notation in the section above the general case? If not, then general case is not redundant, thus it is needed. Are you familiar with sigma/pi notation at all? (Igny (talk) 00:36, 30 May 2009 (UTC))

I am familiar with the notation, but general cases do not require it (as far as I know – do correct me if I am wrong). Why must it be so complex? —Anonymous Dissident^Talk 01:00, 30 May 2009 (UTC)

Can you rewrite the general case section without using sigma/pi? What will you use then, the dots ($\ldots$)? Looks like sigma/pi notation was invented specifically for cases like this. (Igny (talk) 01:41, 30 May 2009 (UTC))

My point is that I don't think recursiveness is required for the general case. —Anonymous Dissident^Talk 01:42, 30 May 2009 (UTC)

I do not understand, recursiveness? What is that? Why should it be required? (Igny (talk) 01:49, 30 May 2009 (UTC))

What I meant to say is that one can give a general case without having to use the capital pi or sigma to signify repetition. This is going nowhere. i think the general case looks okay in the overview section. —Anonymous Dissident^Talk 02:15, 30 May 2009 (UTC)

(Reindend) Oh, I got it. But that is one particular case where log differentiation helps the most, that is when you have a product of many functions. (Igny (talk) 03:31, 30 May 2009 (UTC))

Why natural logs?

All the examples include natural logs why ❓ Uddhav9 (talk) 16:06, 21 May 2020 (UTC)

I think, probably because that is what the article is about. In mathematics, the "logarithmic function" implicitly involves the natural logarithm—see, for instance, Logarithm#Analytic properties. - DVdm (talk) 16:22, 21 May 2020 (UTC)