imo class 12 continuity and differentiability

The derivative of sin⁻¹x with respect to x is:

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The derivative of sin⁻¹x with respect to x is:

  • A. 1 / √(1 + x²)
  • B. −1 / √(1 − x²)
  • C. 1 / √(1 − x²)
  • D. 1 / (1 + x²)

Answer: C) 1 / √(1 − x²)

Explanation: This is a standard formula: d/dx (sin⁻¹x) = 1 / √(1 − x²).

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