  We obtain Weyl type asymptotics for the quantised derivative $\dbar f$ of a
function $f$ from the homgeneous Sobolev space $\dot{W}^1_d(\mathbb{R}^d)$ on
$\mathbb{R}^d.$ The asymptotic coefficient $\|\nabla f\|_{L_d(\mathbb R^d)}$ is
equivalent to the norm of $\dbar f$ in the principal ideal
$\mathcal{L}_{d,\infty},$ thus, providing a non-asymptotic, uniform bound on
the spectrum of $\dbar f.$ Our methods are based on the $C^{\ast}$-algebraic
notion of the principal symbol mapping on $\mathbb{R}^d$, as developed recently
by the last two authors and collaborators.
