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AP EAMCET2013MathematicsDifferentiation

If f(x)= 1 1+ 1 x and g(x)= 1 1+ 1 f(x) , then g^ (2) is equal to

Options

  1. A1 5
  2. B1 25
  3. C5
  4. D1 16

Correct answer

B. 1 25

Step-by-step solution

aligned & f(x)= 1 1+ 1 x = x 1+x & and g(x)= 1 1+ 1 f(x) = 1 1+ 1+x x = x 2 x+1 & g^ (x)= (2 x+1) 1-x(2) (2 x+1)^2 = 1 (2 x+1)^2 & Now, g^ (2)= 1 (4+1)^2 = 1 25 aligned

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