I've had a look on the code again and it seems that currently only the NonLinearLSQFitter uses the analytical
derivative. All the other fitters don't, except for the LinearLSQFitter to set up the coefficient matrix. In principle the other Scipy functions take a derivative function, but currently this seems not to be implemented for the JointFitter and SLSQPFitter: No analytical derivative is passed to the minimizers and also the wrappers for the derivatives, that manage the constraints etc. are missing. Is this correct?
At first sight the handling of constraints seemed quite complicated, so I didn't want to work on this...