I'm following the open courseware content on Machine Learning from Stanford University. In the lecture notes, it is given that

$$\Delta_A \ tr(ABA^TC) = CAB + C^TAB^T$$

which I tried but couldn't prove easily. It is not required to follow the course content but I just wondered and wanted to learn its proof. Any suggestions?

Update: $A$, $B$, and $C$ are matrices and $\Delta_A$ is the gradient operation on matrix $A$.