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JEE Main202325 Jan 2023Morning ShiftMathematicsDifferentiationActual

Let y x = 1 + x 1 + x 2 1 + x 4 1 + x 8 1 + x 16 . Then y ' - y " at x = - 1 is equal to

Options

  1. A976
  2. B464
  3. C496
  4. D944

Correct answer

C. 496

Step-by-step solution

Given, Function y x = 1 + x 1 + x 2 1 + x 4 1 + x 8 1 + x 16 Now multiplying and dividing by 1 - x both side we get, 1 - x y x = 1 - x 1 + x 1 + x 2 1 + x 4 1 + x 8 1 + x 16 ⇒ y 1 - x = 1 - x 32 ⇒ y - x y = 1 - x 32   . . . . . . ( 1 ) Now differentiating equation 1 on both sides with respect to x we get, y ' - x y ' - y = - 32 x 31 . . . . . . . ( 2 ) Now at x = - 1 ⇒ y ' ( - 1 ) = 16 Now differentiating equation 2 with respect to x on both sides we get, ⇒ y " - x y " -

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