Does differential order matter?

1. Sep 3, 2011

quietrain

is this the same? why are they the same? do the order of differential not matter?

d/dxi (dyj / dxj) = d/dxj (dyj / dxi)

where LHS : differentiate yj w.r.t xj first, then xi

while RHS: differentiate yj w.r.t xi first, then xj

thanks!

2. Sep 4, 2011

HallsofIvy

As long as f and its first and second derivatives are continuous, in some neighborhood of a point, the "mixed" derivatives
$$\frac{\partial f}{\partial x\partial y}$$
and
$$\frac{\partial f}{\partial y\partial x}$$
are equal at that point.

3. Sep 6, 2011

quietrain

is this a total differential function? or is it just a normal differential property?

i seem to be mixing everything up :(

4. Sep 6, 2011

HallsofIvy

I have no idea what you are asking. I don't know what you mean by "total differential function" (I do know what a total differential is) or 'normal differential property".

There is no "total differential" in this problem. It is entirely a property of partial derivatives.

5. Sep 7, 2011

quietrain

ah i see than kyou