the derivation of the rotation matrix W with respect to the Lie algebra

[ZZy129326999]

I would like to ask you about the derivation of the rotation matrix W with respect to the Lie algebra in "MonoGS". Why can it be derivated directly in this way? Why not derive W@Sigma (3D covariance)? Thank you very much!

[ZZy129326999]

Can I understand that the corresponding Lie algebra cross-product rotation matrix is ​​obtained through the rotation matrix as the derivative of the rotation matrix, and then the derivative of the rotation matrix is ​​used to derive the three rotation components of the Lie algebra respectively?