I used matrix derivatives in grad school a lot (my dissertation was on nonconvex optimization) and I'm not sure I've ever needed an entire textbook. Matrix calculus is just plain calculus with a few extra rules to generalize it to matrices/vectors.
(to be effective, you do need to know the rules of matrix algebra however)
http://www.gatsby.ucl.ac.uk/teaching/courses/sntn/sntn-2017/...
I used matrix derivatives in grad school a lot (my dissertation was on nonconvex optimization) and I'm not sure I've ever needed an entire textbook. Matrix calculus is just plain calculus with a few extra rules to generalize it to matrices/vectors.
(to be effective, you do need to know the rules of matrix algebra however)