If $f_{xy}(x,y)$ and $f_{yx}(x,y)f_{xy}
(a,b)=f_{yx}
(a,b)$, find a function whose partial derivatives are the same but one of them is not continuous. Which of the following functions satisfies this condition?

A) $f(x,y)=xy$
B) $f(x,y)=x^2+y^2$
C) $f(x,y)=\sin(xy)$
D) $f(x,y)=e^{xy}$