Mathematics

Problem

The variables

x

and

y

(with

x>0

and

y>0

) satisfy

x^{y}y^{x}=e^{x+y}

. Which of the following gives

\dfrac{dy}{dx}

? a)

\displaystyle\frac{1-\dfrac{y}{x}+\ln y}{\ln x+\dfrac{x}{y}-1}

\displaystyle\frac{\dfrac{y}{x}+\ln y-1}{1-\ln x-\dfrac{x}{y}}

\displaystyle\frac{1-\dfrac{y}{x}-\ln y}{\ln x+\dfrac{x}{y}-1}

\displaystyle\frac{1-\dfrac{y}{x}-\ln y}{\ln x-1}