Answers

2015-03-23T22:40:22+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
F(x) = | x |
       =  x  ,  for x ≥ 0
       = - x ,  for x ≤ 0

f( Log x) =  | Log  x |
         = Log x ,    for  1 < x ≤ ∞
         = 0  for x = 1
         = - Log x    for  0 < x < 1
         = undefined  for  x ≤ 0

The function f (Log x) exists in (0, ∞).  It is continuous at all points.  Let us find the derivative from left side and right side of x = 1.

Right side Differential coefficient for x > 1:

\frac{d}{dx}f(Log\ x)=\frac{d}{dx}Log\ x=\frac{1}{x},\ \ for\ x>1

Left side differential coefficient for 0< x < 1 :

\frac{d}{dx}(-log\ x)=-\frac{1}{x},\ \ for\ \ 0 < x < 1

At x = 1,  the derivative from right side is 1 and from left side is -1.  So there is no derivative defined for x = 1. Otherwise, it is defined as:

Differential coefficient of f (Log x) : 
       1/x  for  x > 1
       undefined for x = 1
       -1/x  for  0 < x < 1
       undefined for x <= 0

So the answer is :

           it is     1/x * |x-1|/(x-1)  defined  for  x > 0

\frac{1}{x}*\frac{x-1}{|x-1|},\ \ \ x>0

So the answer is none of the given options.

1 5 1
option (b) log x / x is the derivative of Log (Log x).
option c: (x log x)^-1 is the derivative of Log (log x)
correction: option b: log x /x is the derivative of (Log x)^2 / 2.
hope it is more clear now.
click on the blue thank you link above pls