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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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**zetafunc.****Guest**

Thanks. I am particularly confused by the minus sign.

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**zetafunc.****Guest**

Hmm. I think maybe that comes from an illustration.

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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