NDA 2025 · PYQ · Derivatives of inverse trigonometric functions · medium
Let y = sin⁻¹(x − 4x³/27). What is dy/dx equal to?
- A.1/√(9 − x²)
- B.1/√(3 − x²)
- C.3/√(9 − x²)✓ Correct
- D.9/√(9 − x²)
From y = 3 sin⁻¹(x/3), dy/dx = 3·(1/√(1 − (x/3)²))·(1/3) = 1/√(1 − x²/9) = 3/√(9 − x²).
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