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COMEDK20269 May 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx =

Options

  1. A6x^2 1-x^6
  2. B- 6x^2 1-x^6
  3. C3x^2 1-x^6
  4. D- 3x^2 2 1-x^6

Correct answer

D. - 3x^2 2 1-x^6

Step-by-step solution

Substitute x^3 = 2 . Then 1+x^3 = 1+ 2 = 2 And 1-x^3 = 1- 2 = 2 y = ⁻¹ ( 2 + 2 2 - 2 ) y = ⁻¹ ( + - ) Dividing the numerator and denominator by : y = ⁻¹ ( 1 + 1 - ) y = ⁻¹ ( ( 4 + ) ) y = 4 + Since x^3 = 2 , we have = 1 2 ⁻¹(x^3) . y = 4 + 1 2 ⁻¹(x^3) Differentiating with respect to x : dy dx = 1 2 ( - 1 1 - (x^3)^2 ) d dx (x^3) dy dx = - 3x^2 2 1 - x^6 Answer: - 3x^2 2 1-x^6

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