Let . A student computes h'(x)=(2x)(x-4)(5x)+(x^ 2 +1)(1)(5x)+(x^ 2 +1)(x-4)(5).…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let h(x)=(x2+1)(x−4)(5x). A student computes
h′(x)=(2x)(x−4)(5x)+(x2+1)(1)(5x)+(x2+1)(x−4)(5).
Which statement best explains the structure of the three terms on the right-hand side?
(a) The terms correspond to differentiating two of the factors in each term, leaving the third factor unchanged.
(b) Each term arises from differentiating exactly one of the original factors while keeping the other two factors unchanged.
(c) Each term arises from differentiating all three factors simultaneously.
(d) The three terms appear because h is a composition of functions rather than a product.