How can I prove that the function $f:\mathbb{R}^n\to \mathbb{R}$:
$$f(x) = \sin(\log |\log |x||)$$
belongs to $W^{1,n}(B_r(0)),\, r>0,\, 0\neq x \in \mathbb{R}^n\setminus \partial B_1(0)$.
In the norm of the $ f $ derivative I tried some approximation but was unsuccessful.