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Manipal MET2010MathematicsDifferentiation

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

Options

  1. A1 / e
  2. Be
  3. C-1 / e
  4. D0

Correct answer

A. 1 / e

Step-by-step solution

We have, f(x)= _x( x)= ( x) x f^ (x)= x 1 x 1 x - ( x) 1 x ( x)^2 = 1- ( x) x( x)^2 f^ (e)= 1- ( e) e( e)^2 = 1 e

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