Question about derivative calculation for log determinant in InvQuadLogdet backward method

[ogaken1104]

I'm curious about the computation of the derivative of the log determinant in the InvQuadLogdet backward method.

My understanding is that this implementation aligns with Algorithm 2 from Wenger et al, 2021. However, I couldn't find an explicit implementation for computing $\mathrm{tr}(\boldsymbol{\hat{P}}^{-1}\frac{\partial \boldsymbol{\hat{P}}}{\partial\theta})$, which is mentioned on the third line of Algorithm 2.

Is the difference in implementation due to the use of autograd? I appreciate any clarification on this matter.