Talk:Chain rule
From Academic Kids
This page needs a proof and more rigorous maths.
situations for multivariable should be added: if u is a function of x, and y, and both x, and y are functions of t, then,
<math> \frac{du}{dt} = \frac{\partial u}{\partial x} \frac{dx}{dt} + \frac{\partial u}{\partial y} \frac{dy}{dt} <math>
[edit]
New proof
I've replaced the current proof with one I saw somewhere. It relies on nothing but the definition of a derivative and the concept of limits. I believe it is quite rigourous and more formal than the previous one, but if there are any flaws with it feel free to point them out or even restore the old one.
Also, if you think it is too long or verbose then correct it.
Someone42 13:43, 25 May 2005 (UTC)
- Isn't that really just the same proof, though? Written out longer. I don't think it is different from the point of view of rigour. Charles Matthews 14:06, 25 May 2005 (UTC)
- I just reverted the thing. Someone42, this is not a math paper, not a math exam, not a math book. This is a general purpose encyclopedia.
- I appreciate the many hours you put in that proof, I appreciate your knowledge of mathematics, and your desire for rigor.
- However, nobody will read that proof, even mathematicians will gloss over it.
- According to Wikipedia:WikiProject Mathematics/Proofs, proofs are discouraged on Wikipedia to start with, and long formal proofs especially. This has been discussed over and over again, and this seems to be the general view over here.
- If anything, Wikipedia needs less rigor, not more. This is an encyclopedia for the general public and among its audience mathematicians are less than 10% if not less. Oleg Alexandrov 15:25, 25 May 2005 (UTC)
- Oh well, in retrospect I think I did go a little overboard. Someone42 09:25, 26 May 2005 (UTC)
- I can't really agree about 'rigour'. Anything less than a rigorous proof is just an argument/derivation/bootstrapping. However that is not really the issue here. And I agree with Oleg that the need for proofs is not so high. Charles Matthews 15:29, 25 May 2005 (UTC)
- OK, I did not mean that rigurous proofs are bad overall. I am mathematician too, and I hope I know the value of proofs. I was trying to say that on Wikipedia we can get away with something less than full-blown proofs. So I agree that a proof is not a proof unless it is rigurous. Oleg Alexandrov 22:37, 25 May 2005 (UTC)
