<math>\frac{\partial}{\partial x} (\frac{\partial f}{\partial y}) (0,0) = \lim_{x\to 0} \frac{\frac{\partial f}{\partial y} (x,0)-\frac{\partial f}{\partial y} (0,0)}{x}</math>
<math>\frac{\partial f}{\partial y} (0,0)=0 , \ \ \frac{\partial f}{\partial y} (x,0)=\lim_{y\ to 0} \frac{f(x,y)-f(x,0)}{y}=x</math>
אז