Partial Derivative Proof

zetafunc. · 2012-10-20 22:11:01

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 · 2012-10-20 22:55:38

Hi zetafunc.;

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

zetafunc. · 2012-10-20 22:56:55

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 · 2012-10-20 23:03:33

Hi;

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

zetafunc. · 2012-10-20 23:15:51

Thanks. I am particularly confused by the minus sign.

bobbym · 2012-10-20 23:44:37

Hi;

Check here about half way down.

http://www.solitaryroad.com/c352.html

zetafunc. · 2012-10-20 23:59:31

As part of the proof, they are saying that

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

bobbym · 2012-10-21 00:05:34

Hi;

Over here he calls it a definition.

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

zetafunc. · 2012-10-21 00:28:31

Hmm. I think maybe that comes from an illustration.

bobbym · 2012-10-21 02:25:47

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

Math Is Fun Forum

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

Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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

Re: Partial Derivative Proof

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