  Given a $C^\infty$ real manifold $X$ and $\mathcal{C}^m_X$ its sheaf of
$m$-times differentiable real-valued functions, we prove that the sheaf
$\mathcal{D}^{m, r}_X$ of differential operators of order $\leq m$ with
coefficient functions of class $C^r$ can be obtained in terms of the sheaf
$\mathcal{H}om_{\mathbb{R}_X}(\mathcal{C}^m_X, \mathcal{C}^r_X)$ of morphisms
of $\mathcal{C}^m_X$ into $\mathcal{C}^r_X$. The superscripts $m$ and $r$ are
integers.
