The function $f \in W^{1,d} (\mathbb{R}^d)$ which is $f \notin L^\infty (\mathbb{R})$?

Question

Can we construct such $f \in W^{1,d} (\mathbb{R}^d)$ which is $f \notin L^\infty (\mathbb{R})$, for $d\ge2$? Tried several functions e.g. $f(x)=\exp(|x|), x\in \mathbb{R}^d$ over the $\Omega=\{x\in \mathbb{R}^d: |x|<r, \quad \text{for} \quad r>0\}$ but failed. Any idea, please?