Let $U \subset \mathbb{R}^n$ be open, let $a \in U$, and let $f: U \to \mathbb{R}$ be differentiable at $a$ in the Fréchet sense. For every $v,w \in \mathbb{R}^n$ and every $\alpha,\beta \in \mathbb{R}$, the directional derivatives in the directions $v$, $w$, and $\alpha v+\beta w$ exist, and