Mixed Partial Derivative

A Partial Derivative of second or greater order with respect to two or more different variables, for example

$$f_{xy}={\partial^2 f\over\partial x\partial y}.$$

If the mixed partial derivatives exist and are continuous at a point ${\bf x}_0$, then they are equal at ${\bf x}_0$ regardless of the order in which they are taken.

See also Partial Derivative