From the OpenGL documentation:
dFdxFine and dFdyFine calculate derivatives using local differencing based on on the value of p for the current fragment and its immediate neighbor(s).
dFdxCoarse and dFdyCoarse calculate derivatives using local differencing based on the value of p for the current fragment's neighbors, and will possibly, but not necessarily, include the value for the current fragment. That is, over a given area, the implementation can compute derivatives in fewer unique locations than would be allowed for the corresponding dFdxFine and dFdyFine functions.
Which is the difference between them? When should I care?
I understand that both calculates the derivative of the value respect the window coordinates, but I don't understand the method used to computed them.
I guess that they are both implemented in hardware, but could you post a dFdx pseudo-code implementation?