Motivation
\(f(\mathbf{x}) = \boldsymbol{\beta}^\top\mathbf{x}\) \[\frac{df}{d\mathbf{x}} = \begin{bmatrix} \frac{df}{dx_1} \\ \vdots \\ \frac{df}{dx_n} \end{bmatrix} = \begin{bmatrix} \beta_1 \\ \vdots \\ \beta_n \end{bmatrix} = \boldsymbol{\beta}\]
\(\frac{d}{d\mathbf{x}}(\mathbf{x}^\top A \mathbf{x}) = (\mathbf{A} + \mathbf{A}^\top)\mathbf{x}.\)
