If this expression is differentiated with respect to each x, m simultaneous equations are obtained (for the m adjustable parameters):

If F_c is expanded as a truncated Taylor series,

the following equation results:

in which ΔF is (F_obs - F_calc). Rearranging and collecting terms leads to

and, finally,

This is the jth of m normal equations that yield the parameter shifts needed to improve the agreement of F_obs and F_calc. In this expression, the j-index refers to the parameter with which the the derivative is being taken; the i-index refers to the Taylor expansion of F_c for reflection hkl.