The product rule for three functions extends the two-function product rule by treating one pair of factors as a single composite function and applying the two-function rule recursively, yielding a sum of three terms in which the derivative of each factor is taken in turn while the other two factors are left unchanged. This generalizes directly to a product of n functions, where the derivative equals a sum of n terms, each differentiating exactly one factor and leaving all others intact. This belongs to single-variable differentiation rules within calculus, building on the two-function product rule and illustrating a pattern (single-term differentiation summed across all factors) that generalizes across arbitrary products of differentiable functions.
The product rule for three functions extends the two-function product rule by treating one pair of factors as a single composite function and applying the two-function rule recursively, yielding a su…