Some basic question about matrix calculus. Let $X$, $A$, $B$ be real matrices. Let $\operatorname{Tr}$ denote trace. Is \begin{equation} \frac{d }{dX} \operatorname{Tr}(X^T A XB) \end{equation} equal $(A+ A^T)XB$?
If not, How to compute it?
Some basic question about matrix calculus. Let $X$, $A$, $B$ be real matrices. Let $\operatorname{Tr}$ denote trace. Is \begin{equation} \frac{d }{dX} \operatorname{Tr}(X^T A XB) \end{equation} equal $(A+ A^T)XB$?
If not, How to compute it?