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Manipal MET2018MathematicsDifferentiation

If f(x)= x+ x x- x , f^ ( 2 ) is equal to

Options

  1. A2(x x+ x) (x- x)^2
  2. B2(x x+ x) (x- x)^2
  3. C-2(x x+ x) (x+ x)^2
  4. DNone of these

Correct answer

C. -2(x x+ x) (x+ x)^2

Step-by-step solution

Given, f(x)= x+ x x- x On differentiating w.r.t. x , we get aligned f^ (x) & = [ array c (x- x)(1- x) -(x+ x)(1+ x) array ] (x- x)^2 & = -2 x x-2 x (x- x)^2 aligned

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