Find all points $(x_1,x_2,\ldots,x_k) = x \in \mathbb{R}^k$ such that $f(x)=|x_1 \cdot x_2 \cdots x_k|$ is a differentiable function.
I know that if $\forall i, x_i \neq 0$ then this function is differentiable. I don't know what about rest of points.