A continuous function $f$ such that $\frac{\partial f}{\partial x}$ does not exists but $ \frac{\partial^2 f}{\partial x\partial y}$ exists Does there exist a continuous function $f:\mathbb R^2\to \mathbb R$ such that $\displaystyle \frac{\partial f}{\partial x}$ does not exists but $\displaystyle \frac{\partial^2 f}{\partial x\partial y}$ exists.
I think yes. But I am unable to find an example of such function. Can anyone help me ?

The function $f: R^2 \to R$ where $f(x, y) = |x|+xy$ is an example
See that for the following function $$f_{yx} = 1$$ for every $(x, y) \ \epsilon \ R^2$ 
But $f_x$ doesn't exist at the following set of points $\{ (0, y) \ \epsilon \ R^2 \ | \ y \ \epsilon \ R \} $ 
Thus for the set $\{ (0, y) \ \epsilon \ R^2 \ | \ y \ \epsilon \ R \} \subset R^2$, $f_{yx}$ exists but $f_x$ doesn't exist 
