For which $k \in \mathbb{N}$ and $p \in[1,\infty]$ is $u \in W^{k,p}(B_1(0))$?

Question

Let $u: \overline B_1(0)\subset\mathbb{R^2}\to\mathbb{R}$ defined by
$$u(x_1,x_2)=x_1x_2(1-\sqrt{x_1^2+x_2^2})$$ For which $ k \in \mathbb{N} $ and $ p \in[1,\infty] $ is $ u \in W^{k,p}(B_1(0)) $ ? I don't have any clue. Thanks for helping !