Brainlet filter

let $G=\langle \mathscr{D(\mathbb{R}),+} \rangle$ (where $\mathscr{D}$ is the group of differentiable functions)
$H= \langle \{f\in\mathscr{D(\mathbb{R})} : \frac{df}{dx}$ is constant $\},+\rangle$
Show that $H$ is a subgroup of $G$