12.21.1. - Introduction
Your fitting function can be expressed as y = f(b1, b2, ... bm; x1, x2, ... xm) where the bi are the parameters to be fit and the xi are the independent variables. (Most often, users have only one independent variable.) The fitting algorithm requires derivatives of the fitting function with respect to each fitted parameter. That is, values of ∂ y = f(b1, b2, ... bm; x1, x2, ... xm) / ∂ bi for each bi are needed. If you don't supply the derivatives analytically, the program will calculate them numerically. It is generally more efficient if you supply the derivatives, since numerical evaluation requires an additional call of your fitting equation for each derivative for each point. You can supply derivatives for some of the parameters, though, and let the program calculate them for others.