$\mathbf{x}\in\R^m,\quad \mathbf{A}\in\R^{n\times m};\bold{A}\bot\bold{x}\rightarrow \bold{A}\cdot\bold{x}=0$ 이라 하자.
$$ \mathbf{y}=\bold{A}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=\bold{0} \\\mathbf{y}=\bold{Ax}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=\bold{A} \\\mathbf{y}=\bold{xA}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=\bold{A}^T \\\mathbf{y}=\bold{x^T}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=\bold{I}_m \\\mathbf{y}=\bold{x^Tx}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=2\bold{x}^T \\\mathbf{y}=\bold{x^TAx}\rightarrow\frac{\partial \bold{y}}{\partial \bold{x}}=2\bold{x}^T\bold{A} $$