A) e
B) \[\frac{1}{e}\]
C) 1
D) None of these
Correct Answer: B
Solution :
\[f(x)={{\log }_{x}}(\log x)=\frac{\log (\log x)}{\log x}\] Þ \[f'(x)=\frac{\frac{1}{x}-\frac{1}{x}\log (\log x)}{{{(\log x)}^{2}}}\Rightarrow f'(e)=\frac{\frac{1}{e}-0}{1}=\frac{1}{e}\].
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