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AP EAMCET202125 Aug 2021Morning ShiftMathematicsDifferentiationActual

If y= ⁻¹ [x 1-x - x 1-x^2 ] and 0 < x < 1 , then d y d x is equal to

Options

  1. A1 2 1-x^2 - 1 x 1-x^2
  2. B1 1-x^2 - 1 2 x-x^2
  3. C1 2 x-x^2 + 1 1-x^2
  4. D-1 1-x^2 - 1 x 1-x^2

Correct answer

B. 1 1-x^2 - 1 2 x-x^2

Step-by-step solution

We have, aligned ve, y & = ⁻¹ (x 1-x - x 1-x^2 ) y & = ⁻¹ x- ⁻¹ x d y d x & = 1 1-x^2 - 1 1-x 1 2 x d y d x & = 1 1-x^2 - 1 2 x-x^2 aligned

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