Question 1 • AP Calculus AB - MA5186 A
Use the product rule: if f(x) = u(x)v(x), then f′(x) = u′(x)v(x) + u(x)v′(x). For u(x) = 9x³ − 2 and v(x) = x + 3, this gives f′(x) = 27x²(x + 3) + (9x³ − 2)(1). Expanding and combining terms gives 36x³ + 81x² − 2, which is choice A.
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