I would like to calculate $\frac{\partial \mathbf{y}}{\partial \mathbf{w}}$ where $\mathbf{y} = \mathbf{A}(\mathbf{w} \odot \mathbf{x})$. The vectors $\mathbf{y}$ and $\mathbf{w}$ are complex-valued with dimension Nx1 and $\mathbf{A}$ is a NxN Hermitian matrix. The symbol $\odot$ represents point-wise multiplication.
I have tried to calculate this by using the differential approach but I obtain $d\mathbf{y}=\mathbf{A}(\mathbf{x} \odot d\mathbf{w})$ and do not know how to continue to obtain the differential.
Let $$X=\operatorname{Diag}(x)$$ Then we have $$\eqalign{ y &= AXw \cr dy &= AX\,dw \cr \frac{\partial y}{\partial w} &= AX \cr }$$