秩的交换性，转置不影响

\begin{align*}

\frac{\partial\mathrm{tr} AX}{\partial X}&=A^T,&\frac{\partial\mathrm{tr} \left(AXB\right)}{\partial X}&=A^TB^T,\\

\frac{\partial\mathrm{tr} \left(X^TAX\right)}{\partial X}&=\left(A^T+A\right)X,&\frac{\partial\mathrm{tr} \left(X^TAXB\right)}{\partial X}&=AXB+A^TXB^T,

\end{align*}