Jacobian of depth error in dense visual SLAM

[lanfeiying]

Hi,
I have a question about the jacobian derivation of the depth error function in this paper:
Dense Visual SLAM for RGB-D Cameras (C. Kerl, J. Sturm, D. Cremers), In Proc. of the Int. Conf. on Intelligent Robot Systems (IROS), 2013.

My derivation is presented below:

I did this in my code, but it doesn't work.
I don't find any material about the derivation of this jacobian. Could you help me check this derivation?
I even implemented it using AutoDifferentiation, but it doesn't work.

[lanfeiying]

I only used geometric error without photometric error, this system doesn't optimize the pose.