If log_e y = 3 sin⁻¹x, then (1 − x²)y″ − xy′ at x = 1/2 is equal to :

JEE Main 2024 Mathematics question

If y = 3 sin⁻¹x, then (1 − x²)y″ − xy′ at x = 1/2 is equal to :

Answer: (D)

y = , so y′ = 3y/√(1 − x²). Differentiating (1 − x²)y′² = 9y² gives, after

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Question ID VK-016458