A) \[\frac{1}{x}\]
B) \[\frac{1}{ax}\]
C) \[\frac{1}{x}{{\log }_{x}}a\]
D) \[\frac{1}{a}{{\log }_{e}}x\]
E) \[\frac{1}{x}{{\log }_{a}}e\]
Correct Answer: E
Solution :
\[y={{\log }_{a}}x,\]\[x>0\] \[\Rightarrow \] \[y=\frac{\log x}{\log a},x>0\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{1}{x\log a},x>0\] \[=\frac{1}{x}{{\log }_{a}}e\]
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