x^y=e^(lnx^y)=e^(ylnx)
y^x=e^(xlny)
两边求导
e^(ylnx)(y'lnx+y/x)+e^(xlny)(lny+xy'/y)=0
y'=-x^y/(y^2+xyy^xlny)/(yxx^ylnx+xy^x)
yx^ylnx+y^x≠0
x^y=e^(lnx^y)=e^(ylnx)
y^x=e^(xlny)
两边求导
e^(ylnx)(y'lnx+y/x)+e^(xlny)(lny+xy'/y)=0
y'=-x^y/(y^2+xyy^xlny)/(yxx^ylnx+xy^x)
yx^ylnx+y^x≠0