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JEE Main20207 Jan 2020Evening ShiftMathematicsDifferentiationActual

Let y = y x be a function of x satisfying y 1 - x 2 = k - x 1 - y 2 where k is a constant and y 1 2 = - 1 4 .Then d y d x at x = 1 2 , is equal to

Options

  1. A- 5 4
  2. B- 5 2
  3. C2 5
  4. D5 2

Correct answer

B. - 5 2

Step-by-step solution

x = 1 2 , y = - 1 4 ⇒ x y = - 1 8 y . - 2 x 2 1 - x 2 + y ' . 1 - x 2 = 0 - 1 . 1 - y 2 + x . - 2 y 2 1 - y 2 y ' - x y 1 - x 2 + y ' 1 - x 2 = - 1 - y 2 + x y . y ' 1 - y 2 y ' 1 - x 2 - x y 1 - y 2 = x y 1 - x 2 - 1 - y 2 y ' 3 2 + 1 8 . 15 4 = - 1 8 . 3 4 - 15 4 y ' 45 + 1 2 15 = - 1 + 45 4 3 y ' = - 15 2 3 = - 5 2

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