A) 0
B) 1
C) e
D) 1/e
Correct Answer: D
Solution :
[d] \[\because \,\,\,ln\,\,x={{\log }_{e}}x,so\] \[f(x)={{\log }_{x}}({{\log }_{e}}x)=\frac{\log (\log x)}{\log x}\] \[\Rightarrow \,\,\,f'(x)=\frac{\log x\left( \frac{1}{x\log x} \right)-\log (\log \,x).\frac{1}{x}}{{{(\log \,x)}^{2}}}\] \[\therefore \,\,\,\,f'(e)=\frac{1/e-0}{{{(1)}^{2}}}=\frac{1}{e}\]
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