A) \[\left( x+\frac{1}{x} \right)\]
B) \[\frac{\left( 1+\frac{1}{{{x}^{2}}} \right)}{\left( 1+\frac{1}{x} \right)}\]
C) \[\frac{\left( 1-\frac{1}{{{x}^{2}}} \right)}{\left( x+\frac{1}{x} \right)}\]
D) \[\left( 1+\frac{1}{x} \right)\]
Correct Answer: C
Solution :
\[\frac{d}{dx}\left\{ \log \left( x+\frac{1}{x} \right) \right\}=\frac{1}{x+\frac{1}{x}}\times \frac{d}{dx}\left( x+\frac{1}{x} \right)=\frac{1}{\left( x+\frac{1}{x} \right)}\left( 1-\frac{1}{{{x}^{2}}} \right)\]
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