On page 79 (or page 5) of this [this paper][1] the gradient of the SSE of the Geodesic model is described explicitly. My question is how are these equitations derived in detail; where can I find the computations?

Moreover, if I wanted to solve a contained version of this equation how would can I modify the final solution based on my constraints? [1]: https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCYQFjAB&url=http%3A%2F%2Fwww-sop.inria.fr%2Fasclepios%2Fevents%2FMFCA11%2FProceedings%2FMFCA11_3_1&ei=O-wIVbv0LYHZggTzvQM&usg=AFQjCNEp9Q4TMuDE9LgJoL7KkMvYQwlROg&sig2=mjetJWb7_lXBRNCd51eGag&bvm=bv.88198703,d.eXY

On page 79 (or page 5) of this this paper the gradient of the SSE of the Geodesic model is described explicitly. My question is how are these equitations derived in detail; where can I find the computations?

Moreover, if I wanted to solve a contained version of this equation how would can I modify the final solution based on my constraints?