So, my calculus teacher just said in class today that, fxy = ((δ^2)f)/(δxδy) is true.

Where exactly is this true?

Thanks.

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- Oct 20th 2011, 03:07 PMbagels0Where is this statement true?
So, my calculus teacher just said in class today that, fxy = ((δ^2)f)/(δxδy) is true.

Where exactly is this true?

Thanks. - Oct 20th 2011, 03:13 PMTheChazRe: Where is this statement true?
Not sure exactly what you're saying, but it brings this to mind.

Symmetry of second derivatives - Wikipedia, the free encyclopedia - Oct 21st 2011, 10:29 AMHallsofIvyRe: Where is this statement true?
I think what was meant was that . If that is what was meant, it is

**always**true- those are different notations for the same thing.

If those really are then I would guess that they refer to "small" changes in x, y, and f and so that is an approximation to but is exact in the case that f is a linear function of x and y.

A third possibility is that your teacher was saying that which is the same as saying that - that is that the "mixed" second derivative are equal- independent of the order of differentiation. That is true as long as the second partial derivatives are continuous. - Oct 21st 2011, 12:42 PMSorobanRe: Where is this statement true?
Hello, bagels0!

Quote:

What an UGLY way to write that identity!

Note that: .

And so the claim is that: .

This is true for**all**functions,