> [!NOTE] Lemma > Let $\underline{u}:\mathbb{R}\to \mathbb{R}^{3}$ and $\underline{v}:\mathbb{R}\to \mathbb{R}^{3}$ be [[Fréchet Differentiation|differentiable vector functions]]. Then their [[Cross Product in Real 3-Space|cross product]] is differentiable and its derivative is given by $\frac{d}{dt} [\underline{u}(t) \times \underline{v}(t)]=\underline{u}(t) \times \frac{d}{dt} \underline{v}(t) + [\frac{d}{dt} \underline{u}(t) ] \times \underline{v}(t)$ **Proof**: ...