隐函数求导 x+y-e^xy=0

题目

隐函数求导 x+y-e^xy=0
其实他让求的是dy/dx

答案

dx/dx+dy/dx-e^(xy)(y+x*dy/dx)=0
=>dy/dx*(1-xe^(xy))=-1+y*e^(xy)
=>dy/dx=[-1+y*e^(xy)]/[1-xe^(xy)]=(xy+yy-1)/(1-xx-xy)