This source on slide 38 on receiver plane depth bias I can find compute a matrix (Jacobian of screen space uv derivatives) which is used to transform the screen space depth derivatives from screen space to texture space.
But why does this work? I'm not familiar with the usage of Jacobian matrices and how they relate to coordinate system transformations. Does the basic Jacobian shown in the slide transform from texture space to screen space, or why does it have to be inverse-transposed (I suppose of the former was true it could just be inverted?).