Limits Continuity And Differentiability Question 40
Question: If $ f(x)={\log _{x}}(Inx) $ , then at $ x=e,f’(x) $ equals-
Options:
A) 0
B) 1
C) e
D) 1/e
Show Answer
Answer:
Correct Answer: D
Solution:
$ \because lnx={\log _{e}}x,so $
$ f(x)={\log _{x}}({\log _{e}}x)=\frac{\log (\log x)}{\log x} $
$ \Rightarrow f’(x)=\frac{\log x( \frac{1}{x\log x} )-\log (\log x).\frac{1}{x}}{{{(\log x)}^{2}}} $
$ \therefore f’(e)=\frac{1/e-0}{{{(1)}^{2}}}=\frac{1}{e} $
BETA
