When Are Partial Derivatives Continuous?

[omri3012]

Hallo,
What is the condition for partial derivatives to be continuous (if I have function f(x,y))?
Thanks,
Omri

 

[Astronuc]

Is the partial derivative a continuous function?

For example, does ${\partial y}/{\partial x} = f(x,y)$?

If so, then what is the condition that f(x,y) be continous?

and then apply this to higher order partials ${\partial^n y}/{\partial x^n}$

 

[HallsofIvy]

Hallo,
What is the condition for partial derivatives to be continuous (if I have function f(x,y))?
Thanks,
Omri

That question is a bit strange. There are a number of things that are true if the partials are continuous (mixed derivatives the same, for instance) but I don't know of any that says "IF a condition is true THEN the partials are continuous".