Standard Results of Matrix Calculus

No	$\mathbf{y}$	$\frac{\partial \mathbf{y}}{\partial \mathbf{x}}$
1	$\mathbf{Ax}$	${\mathbf{A}}^T$
2	${\mathbf{x}}^T\mathbf{A}$	$\mathbf{A}$
3	${\mathbf{x}}^T\mathbf{x}$	$2\mathbf{x}$
4	${\mathbf{x}}^{T}A\mathbf{x}$	$\mathbf{Ax}+{\mathbf{A}}^T\mathbf{x}$
Note that (4), if $\mathbf{A}$ is symmetric, it will become $2\mathbf{Ax}$.