Clairaut's Theorem

Theorem
Let $f \left({x, y}\right)$ be a function of the two independent variables $x$ and $y$.

Let $f \left({x, y}\right)$ be continuous.

Let the partial deriviatives of $f$ also be continuous.

Then:
 * $\dfrac {\partial^2 f}{\partial x \partial y} = \dfrac {\partial^2 f}{\partial y \partial x}$