Could someone solve the question and explain me
Let $\omega=(-1,1)\times (-1,1)$ and $f,g:\omega \to \mathbb{R}$ are defined by
$$f(x,y) = \begin{cases} 1, & \text{if $x$ $\le$ 0} \\[2ex] 0, & \text{anywhere else} \end{cases}$$ and
$$g(x,y) = \left\lVert x-y \right\rVert.$$
Determine whether $\frac{\partial f}{\partial x}$, $\frac{\partial f}{\partial y}$, $\frac{\partial g}{\partial x}$, $\frac{\partial g}{\partial y}$ exists weakly and state it if they exist.
Do I need to learn distributions to understand this ?