  Let $\mathcal{R}$ be an $\mathrm{NIP}$ expansion of $(\mathbb{R},<,+)$ by
closed subsets of $\mathbb{R}^n$ and continuous functions $f : \mathbb{R}^m \to
\mathbb{R}^n$. Then $\mathcal{R}$ is generically locally o-minimal. It follows
that if $X \subseteq \mathbb{R}^n$ is definable in $\mathcal{R}$ then the
$C^k$-points of $X$ are dense in $X$ for any $k \geq 0$. This follows from a
more general theorem on $\mathrm{NIP}$ expansions of locally compact groups,
which itself follows from a result on quotients of definable sets by
equivalence relations which are externally definable and $\bigwedge$-definable.
We also show that $\mathcal{R}$ is strongly dependent if and only if
$\mathcal{R}$ is either o-minimal or
$(\mathbb{R},<,+,\alpha\mathbb{Z})$-minimal for some $\alpha > 0$.
