Question

@rational

Answer 1

Say you have this \[\frac{ \partial f }{ \partial x \partial y }\] does it matter if you take the derivative respect to x or y first?

Answer 2

I remember I was taught y then x or something... I didn't understand why.

Answer 3

That should be partial^2 i guess

Answer 4

Yes, it's with respect to y first, then x. Since the shorthand for this is \[f _{xy}\]

Answer 5

Why though?

Answer 6

It's just standard notation.

Answer 7

If you're doing a determinant it doesn't seem to matter I don't think, I know I'm being very vague haha.

Answer 8

$$
\Large {

\frac{ \partial f^2 }{ \partial x \partial y } = \frac{ \partial f^2 }{ \partial y \partial x }


}
$$

Answer 9

assuming fxy and fyx are both continuous on a disc,
this is called Clairut's theorem

Answer 10

No what perl said is right, that works out, and made me question the notation

Answer 11

Clairaut's Theorem

Answer 12

How does it matter which one you do first when they both are equal ?

Answer 13

That's my question :P

Answer 14

General accepted convention \[\large f_{xy} = (f_x)_y\]

But it really doesn't matter because \(f_{xy} = f_{yx}\) always.

Answer 15

Alright cool, thanks everyone :)