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JEE Main2018MathematicsDifferentiationActual

If x 2 + y 2 + sin y = 4 , then the value of d 2 y d x 2 at the point - 2 , 0 is :

Options

  1. A- 34
  2. B4
  3. C- 2
  4. D- 32

Correct answer

A. - 34

Step-by-step solution

Given x 2 + y 2 + sin y = 4 Differentiating both sides with respect to x , we get 2 x + 2 y + cos y d y d x = 0 ⇒ d y d x = - 2 x 2 y + cos ⁡ y At - 2 ,   0 ,   d y d x =   4 1 = 4 Also, 2 y + cos y d y d x + 2 x = 0 Again differentiating with respect to x , we get 2 y + cos y d 2 y d x 2 + 2 - sin y d y d x 2 + 2 = 0 At - 2 ,   0 ,   d 2 y d x 2 + 2 - 0 4 2 + 2 = 0 ⇒ d 2 y d x 2 = - 34

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