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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

Ok, so I know that it's a differential--a change in the function input value--and that it can be used in approximating the function value at that change by dy = f'(x)dx. So far so good.

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.

El que pega primero pega dos veces.

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

```
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)
```

*Last edited by kylekatarn (2005-10-18 03:05:11)*

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,559

Yes, dx is defined in terms of the limit as the slice size goes to 0. I suppose you can say that dx is an infinitesimal slice of x.

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?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

Thanks kylekaturn. After reading it about 10 times, I think I understand.

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.

El que pega primero pega dos veces.

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

No problem ryos.

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

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