Can you give an example?
Let's say I want to differentiate tr(X^T X), tr is the trace, X is a matrix, and X^T is its transpose. Expand:
tr((X + dX)^T (X + dX)) = tr(X^T X) + 2 tr(X^T dX) + tr(dX^T dX).
https://math.stackexchange.com/questions/3680708/what-is-the-difference-between-the-jacobian-hessian-and-the-gradient
https://carmencincotti.com/2022-08-15/the-jacobian-vs-the-hessian-vs-the-gradient/https://sassafras13.github.io/MatrixExps/
“Thanks to a fabulous video by 3Blue1Brown [1], I am going to present some of the basic concepts behind matrix exponentials and why they are useful in robotics when we are writing down the kinematics and dynamics of a robot.”