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KCET2009MathematicsDifferentiation

If f(x)= _ x² ( _ e x ) , then f^ (x) at x=e is

Options

  1. A1
  2. B1 e
  3. C1 2 e
  4. D0

Correct answer

C. 1 2 e

Step-by-step solution

Given, f ( x )= _ x ² ( _ e x )= 1 2 _ x ( _ e x ) f ( x )= 1 2 _ e _ e x _ e x f ^ ( x )= 1 2 _ e x [ 1 x _ e x ]- _ e _ e x 1 x ( _ e x )² f ^ ( x )= 1 2 1 x - 1 x _ e _ e x ( _ e x )² At x = e , f ^ ( e )= 1 2 1 e - 1 e _ e 1 (1)² f ^ ( e )= 1 2 e

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