I am trying to find the following derivative:
$$ \frac{\partial}{\partial W}W^TW $$
where $W \in \mathbb{R}^{n\times m}$ is a matrix. Also I am interested in finding the associated
$$ \frac{\partial}{\partial W}\|W^TW\|_\mathcal{F}^2 $$
I am aware of the fact that
$$ \frac{\partial}{\partial X}\|X\|_\mathcal{F}^2 = \frac{\partial}{\partial X}Tr(XX^T) = 2X $$
But I am not sure if the derivation in terms of $W$ is possible at all. Please advise.
Thank you very much.