imo class 12 continuity and differentiability

Evaluate the derivative of (tan⁻¹x + cot⁻¹x) with respect to x.

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Evaluate the derivative of (tan⁻¹x + cot⁻¹x) with respect to x.

  • A. 1 / (1 + x²)
  • B. 2 / (1 + x²)
  • C. 0
  • D. x

Answer: C) 0

Explanation: tan⁻¹x + cot⁻¹x = π/2 (a constant) for all real x. The derivative of a constant is 0.

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