I know that function $x \mapsto |x|$ has the following subdifferential
$$\partial f(x) = \begin{cases} 1 &, x>0 \\ [-1,1] &, x=0 \\ -1 &, x<0. \end{cases}$$
for $x \in \mathbb{R}$. However, I have no idea how to find the subdifferential of
$$(x_1, x_2) \mapsto |x_1 + x_2| + |x_1 - x_2|$$
I tried to consider the subdifferential of $|x_1 + x_2|$ but I still failed to find it. If you have any ideas on how to find the subdifferential, please share them with me. Thank you.