$\renewcommand{\v}[1]{\mathrm{vec}\left(#1\right)} \renewcommand{\m}[1]{\mathbf{#1}} \renewcommand{\trace}[1]{\mathrm{trace}\left(#1\right)} \renewcommand{\diag}[1]{\mathrm{diag}\left(#1\right)}$
Suppose we have the diagonal matrix $\mathbf{D} = diag(\mathbf{HW1})$, where $W$ is diagonal and known and $1$ is a column vector with ones. $A$ and $B$ are known matrices, also.
How can we calculate the partial derivative of the following wrt matrix calculus? $$\frac{\partial \trace{\mathbf A \mathbf D^{-1/2} \mathbf B)}}{\partial\m H}$$
This can be written as $$\frac{\partial \trace{\mathbf B\mathbf A \mathbf D^{-1/2} }}{\partial\m H} = \frac{\partial \trace{\mathbf{S} \mathbf D^{-1/2} }}{\partial\m H} = \trace {\frac{\partial {\mathbf{S} \mathbf D^{-1/2}} }{\partial\m H}}$$
Except for the analytical way, I couldn't find out in matrix cookbook something that can show me the way.