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

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

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

(i)	\begin{equation} \forall \, x \in \mathbb{R}^{N \times 1} : L(x) = a^T x \end{equation}

Then $L$ is a D5681: Real function derivative for $f$ on $\mathbb{R}^{N \times 1}$.