  Our goal in this work is to present some function spaces on the complex plane
$\C$, $X(\C)$, for which the quasiregular solutions of the Beltrami equation,
$\bar\partial f (z) = \mu(z) \partial f (z)$, have first derivatives locally in
$X(\C)$, provided that the Beltrami coefficient $\mu$ belongs to $X(\C)$.
