If y = sin⁻¹(3x − 4x³), then dy/dx at x = 1/2 is:
If y = sin⁻¹(3x − 4x³), then dy/dx at x = 1/2 is:
- A. 6/√3
- B. 2/√3
- C. 4/√3
- D. 1/√3
Answer: A) 6/√3
Explanation: Put x = sin θ, then 3x−4x³ = sin 3θ, so y = 3θ = 3 sin⁻¹ x (for appropriate range). dy/dx = 3/√(1−x²). At x=1/2, dy/dx = 3/√(3/4) = 6/√3 = 2√3.
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