Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABeasymcq1 pt

If h(x)=x3sin⁡(x)h(x) = x^3 \sin(x), what is the value of h′(π)h'(\pi)?

A.−π3-\pi^3
B.π3\pi^3
C.00
D.−3π2-3\pi^2

Explanation

Core Concept

Using the product rule, h′(x)=3x2sin⁡(x)+x3cos⁡(x)h'(x) = 3x^2\sin(x) + x^3\cos(x). Evaluating at x=πx=\pi gives 3π2(0)+π3(−1)=−π33\pi^2(0) + \pi^3(-1) = -\pi^3.

Correct Answer

A−π3-\pi^3

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