AP Calculus ABmediummcq1 pt
If f(x) = sin(3x²), then f'(x) = ?
A.cos(3x²)
B.6x cos(3x²)
C.cos(6x)
D.-6x cos(3x²)
Explanation
Core Concept
This requires the chain rule. The derivative of sin(u) is cos(u) times u', where u = 3x². The derivative of 3x² is 6x. So f'(x) = cos(3x²) × 6x = 6x cos(3x²), which is option B. Option A is incorrect because it doesn't include the derivative of the inner function. Option C is incorrect because it doesn't apply the chain rule properly. Option D is incorrect because it has a negative sign, which shouldn't be there.
Correct Answer
B6x cos(3x²)
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