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JEE Main20264 April 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ⁻¹ ( 3 x - 4 x 4 x + 3 x ) + 2 ⁻¹ ( x 1+ 1-x^2 ) , then dy dx at x = 3 2 is equal to:

Options

  1. A3
  2. B-1
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

Let y = y₁ + y₂ y₁ = ⁻¹ ( 3 x - 4 x 4 x + 3 x ) Dividing the numerator and denominator by 4 x : y₁ = ⁻¹ ( 3 4 - x 1 + 3 4 x ) Using the formula ⁻¹ ( A - B 1 + AB ) = ⁻¹A - ⁻¹B : y₁ = ⁻¹ ( 3 4 ) - ⁻¹( x) = ⁻¹ ( 3 4 ) - x Differentiating with respect to x : dy₁ dx = -1 Now, y₂ = 2 ⁻¹ ( x 1+ 1-x^2 ) Substituting x = : y₂ = 2 ⁻¹ ( 1+ ) y₂ = 2 ⁻¹ ( 2 ( /2) ( /2) 2 ^2( /2) ) y₂ = 2 ⁻¹ ( 2 ) = 2 ( 2 ) = = ⁻¹x Differentiating with respect to x : dy₂ dx = 1 1-x^2 At x = 3 2 : dy₂ dx = 1 1 - ( 3 2 )^2 = 1 1 - 3 4 = 1 1 4 = 2

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