How does one evaluate the derivative of a matrix with a tensor $\frac{\partial \operatorname{Tr}[A(\mathrm{Id}\otimes w)]}{\partial w}$?

Question

I am stuck on the following:

$$\frac{\partial \operatorname{Tr}[A(\mathrm{Id}\otimes w)]}{\partial w}=\text{ ?}$$

with $A$ a $d\times d^2$ matrix, $\mathrm{Id}$ the identity matrix of $d\times d$ dimension and $w$ a $d\times 1$ vector.

THANKS!!!