Differentiation Question 435
Question: If $ f(x)={\log _{x}}(\log x), $ then $ f’(x) $ at $ x=e $ is
[IIT 1985; RPET 2000; MP PET 2000; Karnataka CET 2002; Pb. CET 2002]
Options:
A) e
B) $ \frac{1}{e} $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)={\log _{x}}(\log x)=\frac{\log (\log x)}{\log x} $
Therefore $ f’(x)=\frac{\frac{1}{x}-\frac{1}{x}\log (\log x)}{{{(\log x)}^{2}}}\Rightarrow f’(e)=\frac{\frac{1}{e}-0}{1}=\frac{1}{e} $ .
BETA
