A) \[\frac{1}{x{{\log }_{e}}x}\]
B) \[\frac{{{\log }_{e}}7}{x{{\log }_{e}}x}\]
C) \[\frac{{{\log }_{7}}e}{x{{\log }_{e}}x}\]
D) \[\frac{{{\log }_{7}}e}{x{{\log }_{7}}x}\]
Correct Answer: C
Solution :
\[\frac{d}{dx}[{{\log }_{7}}({{\log }_{7}}x)]=\frac{d}{dx}\left( \frac{{{\log }_{e}}({{\log }_{7}}x)}{{{\log }_{e}}7} \right)\] \[\sin \theta =\sin \varphi \].
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