Differentiation of vector norms

$$ \frac{\partial}{\partial \beta} \left(\|F(\beta)\|^2\right) = \frac{\partial}{\partial \beta} \left(F(\beta) \cdot F(\beta)\right) = 2 \left( \frac{\partial}{\partial \beta} F(\beta) \right) \cdot F(\beta) $$ $F(\beta) \in \mathcal{R}^D$, where $D$ is the dimension of $F(\beta)$.