Matrix Calculus (Matrix-vector derivatives)

How to find derivatives of functions consisting of matrices and vectors? For example:
$$f(x) =x^TA^TAx$$
As I understand $$A^TA$$ can be treated as constant? How to treat $$x^T$$
My intuition tells me that somehow derivative should be taken in terms of product, but not sure product of what?
$$x^T(A^TAx)?$$

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