Find dy/dx if y = sin⁻¹(2x√(1 − x²)), assuming suitable domain.
Find dy/dx if y = sin⁻¹(2x√(1 − x²)), assuming suitable domain.
- A. 1 / √(1 − x²)
- B. 2 / √(1 − x²)
- C. −2 / √(1 − x²)
- D. 2x / √(1 − x²)
Answer: B) 2 / √(1 − x²)
Explanation: Substitute x = sin θ. The expression is sin⁻¹(2 sin θ cos θ) = sin⁻¹(sin 2θ) = 2θ = 2 sin⁻¹x. The derivative is 2 / √(1 − x²).
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