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## #1 2012-10-20 22:11:01

zetafunc.
Guest

### Partial Derivative Proof

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?

## #2 2012-10-20 22:55:38

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

### Re: Partial Derivative Proof

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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## #3 2012-10-20 22:56:55

zetafunc.
Guest

### Re: Partial Derivative Proof

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?

## #4 2012-10-20 23:03:33

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

### Re: Partial Derivative Proof

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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## #5 2012-10-20 23:15:51

zetafunc.
Guest

### Re: Partial Derivative Proof

Thanks. I am particularly confused by the minus sign.

## #6 2012-10-20 23:44:37

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

### Re: Partial Derivative Proof

Hi;

Check here about half way down.

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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## #7 2012-10-20 23:59:31

zetafunc.
Guest

### Re: Partial Derivative Proof

As part of the proof, they are saying that

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

## #8 2012-10-21 00:05:34

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

### Re: Partial Derivative Proof

Hi;

Over here he calls it a definition.

http://www.ltcconline.net/greenl/course … iffere.htm

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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## #9 2012-10-21 00:28:31

zetafunc.
Guest

### Re: Partial Derivative Proof

Hmm. I think maybe that comes from an illustration.

## #10 2012-10-21 02:25:47

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

### Re: Partial Derivative Proof

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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