In my current PDE lecture we are considering a smooth function $u: \mathbb{R}^n \rightarrow \mathbb{R}$ and a connected, open subset $U \subseteq \mathbb{R}^n$. Let $\Gamma$ denote the surface of $U$ and for $x \in \Gamma$ $q_1(x), \dots, q_n(x)$ an orthonormal system such that $q_1(x), \dots, q_{n-1}(x)$ are tangential to the surface. $q_n(x)$ points in the normal direction.
The lecture notes say:
Since $\Gamma$ is smooth and $u$ as well as it's normal derivative $\partial_{q_n} u$ are given on all of $\Gamma$ also $\partial_{q_i} u$ and $\partial_{q_i}\partial_{q_n}$ for $1 \leq i < n$ are given.
I don't see where this comes from? Any help is welcome.