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if f(x)=cos -1 [1-(log x) 2 ]/[1+(log x) 2 ] then the value of f’(e)= 1 1/e 2/e 2/e 2

if f(x)=cos-1[1-(log x)2]/[1+(log x)2] then the value of f’(e)=
  1. 1
  2. 1/e
  3. 2/e
  4. 2/e2

Grade:11

1 Answers

Arun
25763 Points
2 years ago
 
Dear student
 
let log x = tan theta
 
hence f(x) = cos^-1 (cos 2 theta) = 2 theta = 2 tan^-1 (logx)
 
hence f’(x) = 2/x(1 + (logx)^2)
 
f’(e) = 2/ e(2) = 1/e

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