If \[{{x}^{y}}={{y}^{x}},\]then \[\frac{dy}{dx}=\] [DSSE 1996; MP PET 1997]

\[\frac{x(x{{\log }_{e}}y-y)}{y(y{{\log }_{e}}x-x)}\]

\[\frac{y(x{{\log }_{e}}y+y)}{x(y{{\log }_{e}}x+x)}\]

\[\frac{y(x{{\log }_{e}}y-y)}{x(y{{\log }_{e}}x-x)}\]

\[\frac{x(x{{\log }_{e}}y+y)}{y(y{{\log }_{e}}x+x)}\]

If \[{{x}^{y}}={{y}^{x}},\]then \[\frac{dy}{dx}=\]

1.	If \[{{x}^{y}}={{y}^{x}},\]then \[\frac{dy}{dx}=\] [DSSE 1996; MP PET 1997]
A.	\[\frac{y(x{{\log }_{e}}y+y)}{x(y{{\log }_{e}}x+x)}\]
B.	\[\frac{y(x{{\log }_{e}}y-y)}{x(y{{\log }_{e}}x-x)}\]
C.	\[\frac{x(x{{\log }_{e}}y-y)}{y(y{{\log }_{e}}x-x)}\]
D.	\[\frac{x(x{{\log }_{e}}y+y)}{y(y{{\log }_{e}}x+x)}\]
Answer» C. \[\frac{x(x{{\log }_{e}}y-y)}{y(y{{\log }_{e}}x-x)}\]

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If \[{{x}^{y}}={{y}^{x}},\]then \[\frac{dy}{dx}=\] [DSSE 1996; MP PET 1997]

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