Talk:Second derivative

Massive mistake & misunderstanding.
What is the rate of change of x with respect to x?

dx/dx=1?, but it is not equal to 1, it is equal to zero, the midmode operating point remaining itself.

This is what is called a non-return to zero, where each reiteration sums itself.

The following, how much is

dx/dx + dy/dy = ?

The answer is ZERO, and not one (1), and especially not two (2), a rate of change with respect to that rate of change neither adding nor subtracting from itself.

It is not a licit operation to take the derivative with respect to oneself, the totality remaining the same around the operating point that is itself, therefore any first & second derivative tests on one variable functions is meaningless when there is no secondary variable.

What is that variable? Exchange y=f(x), take the derivative with respect to x, and then we do have a rate of change with respect to something that is not oneself.

A severe inconsistency in the mathematical use of dx/dx, where Adx/dx=A, ie: dx/dx=1, but dx/dx itself being zero.

Any pertinent explanations or is that another one of those, let´s go to church issues to take up theology instead of math?


 * This is nonsense. dx and dy represent infinitely small (although not zero) quantities, and can so be used almost as normal variables. Both dx/dx and dy/dy are perfectly valid mathematical formulations, which both result in one, provided that dx and dy both make sense, i.e. they are associated with some real (or complex) variables with continuous domains. —Kri (talk) 12:58, 8 July 2013 (UTC)

Relation to first derivative
Shouldn't there be an entry for 2y" = d/dy (y')^2 ? — Preceding unsigned comment added by 178.174.240.2 (talk) 23:42, 14 January 2014 (UTC)

Is the Second derivative the same as the differential?
I never took calculus, but I'm trying to understand the basics. The description of the "Second derivative" makes it sound like it's the same thing as the differential (i.e. the rate of change in the linear function), but this article doesn't make that clear. If this is the case, then may I suggest, as a non-calculus-expert, putting that important fact somewhere in the article (preferably in the opening introductory paragraph), so the reader immediately knows that they are the same thing? It would seem to fit it all together more easily.

Practically drawing tangent to an inflation point
I want to practically (by pencil and paper) draw a tangent to an inflation point. Please tell me about the method of drawing a tangent to an inflation point, because drawing a tangent to the other points is easier and has been studied by me, but no books contain the method to draw the tangent on the inflation point.

Ravishankar Joshi --Ravijoshi99 (talk) 13:47, 26 June 2014 (UTC)

Curvature inconsistency
In this article it is stated that the second derivative of a function is its curvature, whereas on the wiki for curvature it is stated that this is only an approximation that holds when the first derivative is small compared to unity. The latter seems more reasonable, could someone a little more comfortable with maths than me clear this up?

— Preceding unsigned comment added by Mhaagh (talk • contribs) 09:04, 16 March 2015 (UTC)