Weak Derivative of function $\operatorname{sgn}(x_1) + \operatorname{sgn}(x_2)$

Question

I am trying to prove that the function $f(x)=\operatorname{sgn}(x_1) + \operatorname{sgn}(x_2)$ where $x \in {R}^{n}$ is not weakly differentiable on the unit ball, I know that the function $f(t)=\operatorname{sgn}(t)$ has the $2{δ}$ Dirac like distribution derivative but, Is this enough to conclude ?