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COMEDK2024Morning ShiftMathematicsDifferentiationActual

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

Options

  1. A- 1 x^2
  2. B- 1 x
  3. C2 x^2
  4. D- 2 x^2

Correct answer

D. - 2 x^2

Step-by-step solution

Given y = _ e ( x^2 e^2 ) . Using the properties of logarithms, _ e ( a b ) = _ e a - _ e b , we have: y = _ e (x^2) - _ e (e^2) y = 2 _ e x - 2 _ e e Since _ e e = 1 , the expression simplifies to: y = 2 _ e x - 2 Differentiating with respect to x once: dy dx = d dx (2 _ e x - 2) = 2 1 x = 2 x Differentiating with respect to x again to find the second derivative: d^2 y dx^2 = d dx ( 2 x ) = 2 (- 1 x^2 ) = - 2 x^2 Answer: - 2 x^2

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