微积分.若x^y=y^x,则dy/dx.

问题描述:

微积分.若x^y=y^x,则dy/dx.
[x^2-xylnx]/[y^2-xylny]

两边取对数得:ylnx=xlny
两边对x求导得:
(dy/dx)lnx+y/x=lny+(x/y)dy/dx
解得:
dy/dx=[x^2-xylnx]/[y^2-xylny]