求隐函数的导数dy/dx?x^y=y^x
问题描述：
求隐函数的导数dy/dx?
x^y=y^x
答
x^y=y^x e^[ylnx]=e^[xlny] x^y*(ylnx)'=y^x(xlny)' (lnxy'+y/x)=(lny+xy'/y) y'=(lny-y/x)/(lnx-x/y) =(xylny-y^2)/(xylnx-x^2).