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MHT CET202616 April 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ⁻¹ [ x - 1 - x^2 x + 1 - x^2 ] , then dy dx =

Options

  1. A-1 1 - x^2
  2. B1 1 - x^2
  3. C1
  4. D-1

Correct answer

B. 1 1 - x^2

Step-by-step solution

Let x = , which implies = ⁻¹ x . Substituting this into the given expression, we get: y = ⁻¹ [ - 1 - ^2 + 1 - ^2 ] y = ⁻¹ [ - + ] Dividing the numerator and the denominator by , we obtain: y = ⁻¹ [ - 1 + 1 ] Using the trigonometric identity (A - B) = A - B 1 + A B with A = and B = 4 : y = ⁻¹ [ ( - 4 ) ] y = - 4 Substituting back = ⁻¹ x : y = ⁻¹ x - 4 Differentiating with respect to x : dy dx = 1 1 - x^2 - 0 dy dx = 1 1 - x^2 Answer: 1 1 - x^2

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