I am trying to take the second derivative of the inference of the variance of a gaussian process. The problem looks as such:
$\frac{d^2}{dxdx}K_{xx}(x) - K_x(x)^TCK_x(x)$
Where C is not dependent on x.
Taking the derivative of the $K_{xx}$ is trivial, but then the second part is what stumps me. Taking the derivative once, I believe I end up with:
$ 2*K_x(x)^TCK_x'(x)$
I ended up with this by matching it with some of the derivations in the Matrix cookbook and realizing the $K_x'(x)$ has to go there for the size of the matrices to match, but I don't know the exact rule of how it ends up there. I still need to take the derivative of $ 2*K_x(x)^TCK_x'(x)$ once more, which I do not know how.
Can somebody point me to some resources that explain the intuition behind matrix calculus. And help with the second derivative?
Cheers