I would like to take the derivative of the following expression w.r.t. the matrix $A \in \mathbb{R}^{m \times n}$, i.e.,
$$ \frac{\partial \big( \sum_{i=1}^m (Ax)_i \big)}{\partial A}, $$
where $x \in \mathbb{R}^n$. The second answer here gives the derivative of the matrix-vector product w.r.t. the matrix, but, I wasn't sure how it changes with the summation? Though I think that it should work out cleanly since derivative and summation are linear operators and can be interchanged? I am not sure about how the indices would change so any advice regarding that would be much appreciated.