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Question 360011
JEE Mathematics · Hard

Differentiability: JEE Advanced MCQ

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JEE AdvancedHardQuestion 360011

Question

If y = tan⁻¹(2x/(1−x²)), then dy/dx for |x| < 1 is:
  1. A
    2/(1+x²)
    Correct
  2. B
    1/(1+x²)
  3. C
    2(1−x²)/(1+x²)²
  4. D
    1/(1+4x²)

Correct answer

2/(1+x²)

Explanation

Recognize: 2x/(1−x²) = tan(2θ) when x = tan θ. So y = tan⁻¹(tan 2θ) = 2θ = 2tan⁻¹x. dy/dx = 2/(1+x²).

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