  Let $f : [0, 1] \to [0, 1]$ be a piecewise expanding unimodal map of class
$C^{k+1}$, with $k \geq 1$, and $\mu = \rho dx$ the (unique) SRB measure
associated to it. We study the regularity of $\rho$. In particular, points
$\mathcal{N}$ where $\rho$ is not differentiable has zero Hausdorff dimension,
but is uncountable if the critical orbit of $f$ is dense. This improves on a
work of Szewc (1984). We also obtain results about higher orders of
differentiability of $\rho$ in the sense of Whitney.
