This answer states that the differential of a trace function is given by
$d\text{Tr}(f(X)) = f'(X^T):dX$ where the colon $A:B$ means $\text{Tr}(A^TB)$.
How do we prove it? Does any know any reference/textbook that states this?
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1Look here – Jean Marie Jan 28 '23 at 08:56
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You can start from there : https://en.wikipedia.org/wiki/Matrix_calculus#Identities_in_differential_form – Abezhiko Jan 28 '23 at 11:51