Let $f : \mathbb{R}^{N \times 1} \to \mathbb{R}$ be a D4363: Euclidean real function such that

(i)	\begin{equation} \exists \, b \in \mathbb{R}^{N \times 1} : \forall \, x \in \mathbb{R}^{N \times 1} : f(x) = (x - b)^T (x - b) \end{equation}

Let $L : \mathbb{R}^{N \times 1} \to \mathbb{R}$ be a D4364: Real function such that

(i)	$x_0 \in \mathbb{R}^{N \times 1}$ is a D5200: Real column matrix
(ii)	\begin{equation} \forall \, x \in \mathbb{R}^{N \times 1} : L(x) = 2 (x_0 - b)^T x \end{equation}

This result is a particular case of R4960: Strong derivative for euclidean real quadratic form. $\square$