AP Calculus ABeasymcq1 pt
The derivative of f(x) = x³ cos(x) is
A.3x² cos(x) - x³ sin(x)
B.3x² cos(x) + x³ sin(x)
C.x² cos(x) - x³ sin(x)
D.3x² cos(x)
Explanation
Core Concept
This requires the product rule: (uv)' = u'v + uv'. Here u = x³, u' = 3x², v = cos(x), v' = -sin(x). So f'(x) = 3x² cos(x) + x³(-sin(x)) = 3x² cos(x) - x³ sin(x).
Correct Answer
A3x² cos(x) - x³ sin(x)
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