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JEE Main2017MathematicsDifferentiationActual

If y = x + x 2 - 1 15 + x - x 2 - 1 15 , then x 2 - 1 d 2 y d x 2 + x d y d x is equal to

Options

  1. A224   y 2
  2. B125 y
  3. C225 y
  4. D225 y 2

Correct answer

C. 225 y

Step-by-step solution

y = x + x 2 - 1 15 + x - x 2 - 1 15 d y d x = 15 x + x 2 - 1 14 1 + x x 2 - 1 + 15 x - x 2 - 1 14 1 - x x 2 - 1 d y d x = 15 x + x 2 - 1 14 x + x 2 - 1 x 2 - 1 + 15 x - x 2 - 1 14 x - x 2 - 1 x 2 - 1 d y d x = 15 x + x 2 - 1 15 - x - x 2 - 1 15 x 2 - 1 ⇒ x 2 - 1   . d y d x = 15 x + x 2 - 1 15 - x - x 2 - 1 15 ⇒ x x 2 - 1   . d y d x +   x 2 - 1 d 2 y d x 2 = 15 × 15 y x 2 - 1 ⇒ x d y d x + x 2 - 1 d 2 y   d x 2 = 15 x 2 - 1 × 15 y x 2 - 1 = 225 y

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