Find a differential of the following function:
$$f(X) = a^T X B$$
where $B$ and $X$ are $n \times n$ matrices, and $a \in \mathbb{R}^n$.
We have nothing in our script about it and I wasn't able to figure out anything on the internet so far. I think I got an idea on how to produce a derivative corresponding to a vector, but I do not see where to start to differentiate with respect to a matrix? I have to
Show that $g(X)=a^T X^T X B a$ is zero-negligible.
Find the derivative of $g(x)$ from $1.$.
How could I approach $1.$?