MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let q(x)=(x3+2x)2.
(a) Expand q(x) completely to express it as a polynomial in powers of x.
(b) By treating q(x+h)−q(x) algebraically, derive a simplified expression for hq(x+h)−q(x).
(c) Evaluate the limit of your result in part (b) as h→0 and obtain q′(x). Express your final answer in its most factorised form.