In what follows is an arbitrary square matrix and . Derivations can be found e.g. in [PP12]
Notation:
(1)
Derivative of trace:
(2)
Derivative of power:
(3)
Derivative of inverse:
(4)
Derivative of inverse power:
(5)
Derivative of determinant:
(6)
Derivative of exponent (see this StackExchange answer):
(7)
References
[PP12]
K. B. Petersen and M. S. Pedersen, “Matrix cookbook,” 2012. Available: https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf