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AP EAMCET2008MathematicsDifferentiation

If y= ( _e x ) , then x^2 d^2 y d x^2 +x d y d x is equal to

Options

  1. A( _e x )
  2. B( _e x )
  3. Cy^2
  4. D-y

Correct answer

D. -y

Step-by-step solution

Given that, y= ( _e x ) On differentiating w.r.t. x , we get d y d x = ( _e x ) 1 x Again differentiating, we get aligned d^2 y d x^2 & = -x ( _e x ) 1 x - ( _e x ) 1 x^2 & = - ( _e x )- ( _e x ) x^2 aligned Now, x^2 d^2 y d x^2 +x d y d x aligned & = x^2 [- ( _e x )- ( _e x ) ] x^2 & =- ( _e x ) & =-y [from Eq. (i)] aligned

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