This document describes the generalization of the well-known derivative rule for finding the extrema of a function to the case where we have multiple (usually conflicting) objective functions.
We assume that a dependent quantity y can be expressed in terms of a linear function of a number of independent quantities x, i.e. y = ∑j αjxj. Note that this expression does not allow for a constant term. However, this is not a loss of generality: it can be emulated by making one of the independent quantities, say x0, equal to 1 for all points in your dataset.