# Order of partial derivatives

1. Oct 4, 2004

### kuba

Given a scalar-valued function $$f=f(x,y)$$, if it's true that $$\frac{\partial^2 f}{\partial x \partial y}=\frac{\partial^2 f}{\partial y \partial x}$$, what does that tell about function $$f$$? Does it mean that it's continuous, or does it need to be smooth, or...?

2. Oct 4, 2004

### kuba

I'm presuming that the correct answer is that the function $$f$$ must be continuous.

3. Oct 4, 2004

### neutrino

You are right. The partial derivatives upto that order should exist and be continuous at the point under consideration.

4. Oct 4, 2004

### ReyChiquito

Its more than continous, actually it tells you that the function f is differentiable.

$$f(x,y)\in C^{1}$$