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**zetafunc.****Guest**

I came across an interesting tool which would help for differentiating functions involving x and y;

where f is a function of x and y and the deltas denote partial derivatives.

But why is this the case?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi zetafunc.;

I know about that one. It is useful for implicit functions.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Yes, I agree. It was useful for solving the ODEs we were given in class when we had to differentiate annoying functions twice and sub initial conditions, etc... do you remember how it is derived?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

That I do not. I will see if I can find anything.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Thanks. I am particularly confused by the minus sign.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

As part of the proof, they are saying that

is the total differential of the function f(x,y). Why?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Hmm. I think maybe that comes from an illustration.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

It looks like it comes from the total derivative but I can not understand their notation so I can not derive it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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