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JEE Main2017MathematicsDifferentiationActual

If for x ∈ 0 , 1 4 , the derivative of tan - 1 ⁡ 6 x x 1 - 9 x 3 is x ⋅ g x , then g x equals:

Options

  1. A9 1 + 9 x 3
  2. B3 x x 1 - 9 x 3
  3. C3 x 1 - 9 x 3
  4. D3 1 + 9 x 3

Correct answer

A. 9 1 + 9 x 3

Step-by-step solution

Let 3 x 3 2 = y , then y ∈ 0 , 3 8   tan - 1 ⁡ 6 x x 1 - 9 x 3 = tan - 1 ⁡ 2 y 1 - y 2 ⇒   2 tan - 1 ⁡ y = 2 tan - 1 ⁡ 3 x 3 2 Now ⇒ d d x 2 tan - 1 ⁡ 3 x 3 2 = 2 1 + 9 x 3 ⋅ 3 ⋅ 3 2 ⋅ x 1 2 ⇒ d d x 2 tan - 1 ⁡ 3 x 3 2 = 9 1 + 9 x 3   ⋅   x ⇒ x . g x = 9 1 + 9 x 3   ⋅   x ⇒ g x = 9 1 + 9 x 3

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