Math Is Fun Forum

LQ

Real Member

Registered: 2006-12-04

Posts: 1,285

Re: easy proof of the chain rule?

+ 1 million x minus 2 million x^2.... The point is we have x:es here. It doesn't matter if it is divergent or not it is still a bunch of x:es in the long run. Derivate the infinit diverging serie and you will have your answer

It's like hunting a rabbit with infinite size... Some may say you can't... Others say it's a rabbit.

Last edited by LQ (2007-06-04 01:41:01)

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I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: easy proof of the chain rule?

All deriveable functions can be simplified to Ax^a + Bx^b +... + Sx^s

Isn't that so?

sin(x)
e^x

There are so many more examples.

All exp, log and trig functions can be simplified like this. Even roots, unfortunately the term diverge. I can only think of ax^bx that doesn't work. How do you derivate that by the way?

No, you can't.  There are infinite series which can be, yes, but there is no finite series.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

LQ

Real Member

Registered: 2006-12-04

Posts: 1,285

Re: easy proof of the chain rule?

I apologize, ofcourse that's what I meant.

And now to show an example where it cannot be simplified like that.

I don't have any available at the moment, but I'm sure we can find one.

Last edited by LQ (2007-06-04 02:21:48)

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I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: easy proof of the chain rule?

Well the infinite series thing is applied by taking a finite part of it. So Maclaurin series is very useful in getting any digit we want.

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X'(y-Xβ)=0