Matrix differentiation, $x^T A x$ w.r.t $A$

Question

In Gaussian Mixture Models, in order to derive the M-step for covariance matrix, I need this result. I have poor knowledge of matrix calculus and result does not exist in https://en.wikipedia.org/wiki/Matrix_calculus

What is the partial derivative of $x^T A x$ w.r.t $A$?

Answer 1

Note that $$x'Ax = \mathrm{tr}(xx'A) = xx':A,$$ where $:$ is a scalar product on the space of matrices. The derivative wrt $A$ is thus $xx'$.