Once you get used to dx's and dy's and d'whatever... You'll see how much easier and clear the whole subject becomes. If my explanation was a bit difficult for 'newcomers' to understand please apologize me. I'm not a teacher nor tutor - just a student.

BTW do you have calculus or some class related this or you are just curious? (like I was

]]>MathsIsFun, a page on dx would be great. I would say that, instead of following odd rules, it just sort of breaks them sometimes. Though offensive to mathematicians, it's accurate.

]]>But it does seem to follow odd rules at times. Sometimes you can do seemingly illegal things with it, and other times a simple thing is not allowed.

I would like to make a page on this one day. Maybe I could start with figuring the area under a curve, maybe the x^2 curve, starting with large slices and going smaller.

How do the rest of you understand dx?

]]>```
f: A -> B
x -> y = f(x)
dx = lim Δx
Δx->0
dy = lim Δy
Δx->0
Δx dx
f'(x) = lim -- = --
Δx->0 Δy dy
```

```
I{ f(x) dx } : integral of f(x) with respect to x
G: A -> B
x -> y = f(x)
dy
f'(x) = --
dx
dy = f'(x)dx
I{ 1 dy } = I{ f'(x) dx }
y = f(x)
```

Then, my book goes on to give the rules of derivatives in differential notation. An example of this is the power rule: d(u^n) = nu^(n-1)**du**

I've emphasized the du because it seems to have no business being there. You have (nu^(n-1)), which is the rule to find the *exact* derivative of a power function, and then we stupidly approximate it by multiplying by an arbitrary du. And if the derivative we've found really is exact, then wouldn't du=0, thus invalidating our results entirely?

It gets worse in integrals. They insist on a meaningless dx in ALL of them. They tell you to put it on there and then ignore it while you happily integrate, leaving it out of your solution entirely. What?

I'm sorry for ranting. I know I shouldn't be so condescending towards dx, since it's me who doesn't understand, but it makes me angry because I can't find a proper explanation anywhere, so it's something that *obviously* everyone should just understand, but I don't.

It's a conspiracy of mathematicians! Lol, I'm better now. Or I will be, once I understand dx.

]]>