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JEE Main20205 Sep 2020Evening ShiftMathematicsDifferentiationActual

The derivative of tan - 1 1 + x 2 - 1 x with respect to tan - 1 2 x 1 - x 2 1 - 2 x 2 at x = 1 2 is :

Options

  1. A2 3 5
  2. B3 12
  3. C2 3 3
  4. D3 10

Correct answer

D. 3 10

Step-by-step solution

Let x = tan θ y 1 = tan - 1 sec θ - 1 tan θ = tan - 1 tan θ 2 = θ 2 = 1 2 tan - 1 x x = sin ϕ ,    y 2 = tan - 1 2 sin ϕ cos ϕ cos 2 ϕ = tan - 1 ( tan 2 ϕ ) = 2 ϕ = 2 sin - 1 x d y 1 d y 2 = d y 1 / d x d y 2 / d x = 1 1 + x 2 · 1 2 2 · 1 1 - x 2 = 1 - x 2 4 1 + x 2 = 1 - 1 4 4 1 + 1 4 = 3 10

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