Continuity of second partial derivatives: Could $F_{xy}$ be continuous while $F_{yx}$ is not?

Question

THEOREM $3.1$: If $f_{xy}(x, y)$ and $f_{yx}(x, y)$ are continuous on an open set containing $(a, b)$, then $f_{xy}(a, b) = f_{yx}(a, b)$.

My question is: Could $F_{xy}$ be continuous while $F_{yx}$ is not? Is there example for this case ?

Thanks