If \[y={{\left( 1+\frac{1}{x} \right)}^{x}}\], then \[\frac{dy}{dx}=\] [BIT Ranchi 1992]

\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right) \right]\]

\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)-\frac{1}{1+x} \right]\]

\[{{\left( x+\frac{1}{x} \right)}^{x}}\left[ \log (x-1)-\frac{x}{x+1} \right]\]

\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)+\frac{1}{1+x} \right]\]

If \[y={{\left( 1+\frac{1}{x} \right)}^{x}}\], then \[\frac{dy}{dx}=

1.	If \[y={{\left( 1+\frac{1}{x} \right)}^{x}}\], then \[\frac{dy}{dx}=\] [BIT Ranchi 1992]
A.	\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)-\frac{1}{1+x} \right]\]
B.	\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right) \right]\]
C.	\[{{\left( x+\frac{1}{x} \right)}^{x}}\left[ \log (x-1)-\frac{x}{x+1} \right]\]
D.	\[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right)+\frac{1}{1+x} \right]\]
Answer» B. \[{{\left( 1+\frac{1}{x} \right)}^{x}}\left[ \log \left( 1+\frac{1}{x} \right) \right]\]

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If \[y={{\left( 1+\frac{1}{x} \right)}^{x}}\], then \[\frac{dy}{dx}=\] [BIT Ranchi 1992]

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