Given xy=yxx^y = y^xxy=yx, find dydx\frac{dy}{dx}dxdy in terms of xxx and yyy.
y(y−xlny)x(x−ylnx)\frac{y(y - x\ln y)}{x(x - y\ln x)}x(x−ylnx)y(y−xlny)
y(xlny−y)x(ylnx−x)\frac{y(x\ln y - y)}{x(y\ln x - x)}x(ylnx−x)y(xlny−y)
y(ylnx−x)x(xlny−y)\frac{y(y\ln x - x)}{x(x\ln y - y)}x(xlny−y)y(ylnx−x)
x(y−xlny)y(x−ylnx)\frac{x(y - x\ln y)}{y(x - y\ln x)}y(x−ylnx)x(y−xlny)