What is the meaning of dx?

# What is the meaning of dx?

dx would the same as delta x. dy is the change in y of your llinear approximation, so it can be different than delta y, dy = f'(x)dx

Idiots misunderstanding bad notation.

Unless this is the context of differential geometry, in which case it is more acceptable bad notation.

Daily reminder that infinitesimals are heresy and [math]1-0.999...=0[/math].

Fuck off, there is no meaning. It's not a mysterious infintesimal number or whatever, this is a lie "calculus" teachers tell to please the brainlets

Depend on the context, if you are talking about the [math]dx[/math] in [math] \int f(x) dx[/math], it is simply there to tell you the variable you are integrating.

If you are calculating of the differential of a function [math] f [/math] , let say a function of 2 variable, then [math] df(x,y)=\frac{\partial f}{\partial x}(x,y) dx + \frac{\partial f}{\partial y} (x,y) dy[/math], then the dx and dy are map defined as : [math] dx(h,k)=h]/math] and [math]dy(h,k)=k[/math]

Is standard analysis, there is no such thing are infinitesimal change or whatever

A differential form. All the brainlets saying hurr durr infinitely small should kys themselves

it is a very small difference in x, so it is the same as delta x, but with the limit of xf -> xi

in the end, it does not have much numerical value, just algebrical and analytical, you can't calculate a value for it, trying to evaluating the limit gives you 0, and in many times it will be used as a variable

dx is a placeholder for the statement "with respect to delta x, as it gets closer to zero". there's no depth to this. it's like f(x) meaning "the function at the value x". it's all shorthand stuff because mathematicians are too weak willed to write long winded statements and concatenate everything.

in differential geometry (or just advanced calculus) it's a differential form

in basic calculus it's just notation and/or some handwaving bullshit

Something about epsilon and delta or something I dunno lolol just ignore all the dumb proof bits.