Talk:Differential of a function

Title

I'd call it something like Differential (analysis) to deliniate the area in which it is a valid definition. It isn't what people mean by it in topology for instance and it isn't the infinitessmal version. Dmcq (talk) 23:32, 15 August 2009 (UTC)[reply]

Dmcq, there is no book that will tell you a differential has an "infinitessimal version" as in "the differential is an infinitessimal". It is more likely that you will find, if lucky, in some book that the differential is "the ratio of two infinitessimals" multiplyied by a finit increment. Read that carefully.

And then you could find some equation like this one:

dy={\frac {\mathrm {d} y}{\mathrm {d} x}}\Delta x\,

Where ${\frac {\mathrm {d} y}{\mathrm {d} x}}$ is in Leibniz's notation and means "the derivative of y with respect to x."
Notice $dy\neq \mathrm {d} y\,$ . $dy$ is the differential, while $\mathrm {d} y$ is the infinitessimal. We need to differentiate (contradistinguish the variables) because of the notation choosed to represent the derivative.

Considering this other equeality:

\mathrm {d} y={\frac {\mathrm {d} y}{\mathrm {d} x}}\mathrm {d} x\,

I see it is true, whether you take it as Leibniz's notation or not.

The last equality in Leibniz's notation, means that dy (in both sides of the equation) is an infinitesimal. The left side of the equation is NOT the differential dy, IT IS the infinitessimal dy.Usuwiki (talk) 00:04, 16 August 2009 (UTC)[reply]

You better point that convention out in the article clearly. It doesn't seem to follow it so far, in fact you seem to have the opposite and used the upright d for a differential. The notation has been round long before two lots of d's and d traditionally has meant an infinitessmal amount and it has been referred to as a differential. You can deal with it however you like but you'll need to explain what you mean in the article rather than just complain about people misunderstanding it. Dmcq (talk) 00:53, 16 August 2009 (UTC)[reply]

Exactly. You can use whatever d you want as long as you are clear about what notation you are using, if it's Leibniz's one, then you are talking about infinitesimals, if not, then, most likely, you are talking about differentials.Usuwiki (talk) 02:47, 16 August 2009 (UTC)[reply]