  We prove that the tangent space to the $(n+1)$-th Milnor $K$-group of a ring
$R$ is isomorphic to group of $n$-th absolute K\"ahler differentials of $R$
when the ring $R$ contains $\frac{1}{2}$ and has sufficiently many invertible
elements. More precisely, the latter condition is that $R$ is weakly $5$-fold
stable in the sense of Morrow.
