Answer: 2sin x cos x.
- A 2sin x cos x
- B sin²x
- C 2 sin x
- D cos²x
Correct answer: A. 2sin x cos x
Explanation: Chain rule: f'(g(x))×g'(x) = 2sin(x) × cos(x) = 2sinx cosx = sin 2x.
As point Q slides along the curve toward P, the secant line PQ rotates into the tangent line at P, whose slope is the derivative.
Concept context
Rate of change, differentiation rules, and applications