[Math] Derivatives of a the Matrix diagonal function

Question

If A is a not diagonal but symetric matrix and diag() is a function such that returns the diagonal, i.e. diag(A) is a matrix of zeros except on the diagonal. Im interested in the derivative of vec(diag(A)) with respect to x where A is a function of the vector x. So, how do I do This in the best way?

Thanks in advance!

Answer 1

The derivative of the $(i,i)$ entry of $\text{diag}(A)$ is the same as the derivative of the $(i,i)$ entry of $A$. The derivative of the $(i,j)$ entry of $\text{diag}(A)$ for $i \ne j$ is $0$.