Which of the following expressions equals where and are differentiable functions?

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Which of the following expressions equals ddx[p(x)q(x)r(x)]\dfrac{d}{dx}[p(x)q(x)r(x)] where p, q,p,\,q, and rr are differentiable functions? (a) [p′(x)+q′(x)+r′(x)]p(x)q(x)r(x)[p'(x)+q'(x)+r'(x)]p(x)q(x)r(x) (b) p′(x)q(x)r(x)+p(x)q′(x)r(x)p'(x)q(x)r(x)+p(x)q'(x)r(x) (c) p′(x)q(x)r(x)+p(x)q′(x)r(x)+p(x)q(x)r′(x)p'(x)q(x)r(x)+p(x)q'(x)r(x)+p(x)q(x)r'(x) (d) p′(x)q′(x)r(x)+p(x)q′(x)r′(x)+p′(x)q(x)r′(x)p'(x)q'(x)r(x)+p(x)q'(x)r'(x)+p'(x)q(x)r'(x)

Related theory

Browse the problem library