Partial derivative problem on absolute value function Find the first and second order partial derivatives of 
$f(x,y)=|2x^2-y|$.
I start with limit definition but not able to solve.
please help.

$$\frac{\delta f}{dx} = 4x, -\sqrt{2}x \lt y\lt \sqrt{2}x$$
$$\frac{\delta f}{dy} = -1, x \lt -\sqrt{\frac{y}{2}}, x\gt \sqrt{\frac{y}{2}}$$
$$\frac{\delta f}{dx}= -4x, y\lt -\sqrt{2}x, y \gt \sqrt{2}x$$
$$\frac{\delta f}{dy}= 1, -\sqrt{\frac{y}{2}} \lt x\lt \sqrt{\frac{y}{2}}$$
$$\frac{\delta^2 f}{dx^2} = 4, -\sqrt{2}x \lt y\lt \sqrt{2}x$$
$$\frac{\delta^2 f}{dx^2} = -4, y\lt -\sqrt{2}x, y \gt \sqrt{2}x$$
$$\frac{\delta^2 f}{dy^2} = 0 -\infty \lt x\lt \infty$$
$$\frac{\delta^2 f}{dxdy} = \frac{\delta^2 f}{dydx} = 0 -\infty \lt x\lt \infty$$
