AP Calculus ABeasymcq1 pt

The derivative of f(x) = x^3 cos(x) is

A.A) 3x^2 cos(x) - x^3 sin(x)

B.C) x^2 cos(x) - x^3 sin(x)

C.B) 3x^2 cos(x) + x^3 sin(x)

D.D) 3x^2 cos(x)

Explanation

Core Concept

This requires the product rule: (uv)' = u'v + uv'. Here u = x^3, u' = 3x^2, v = cos(x), v' = -sin(x). So f'(x) = 3x^2 cos(x) + x^3(-sin(x)) = 3x^2 cos(x) - x^3 sin(x).

Correct Answer

AA) 3x^2 cos(x) - x^3 sin(x)

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