y=x+e^y和y=cos(xy)-x的微分,详解3Q

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为隐函数微分
1)y=x+e^y
dy=dx+e^ydy
dy/dx=1/(1-e^y)
2)y=cos(xy)-x
dy=-sin(xy)(ydx+xdy)-dx
dy=-[sin(xy)*y+1]dx-sin(xy)*xdy
[1+xsin(xy)]dy=-[ysin(xy)+1]dx
dy/dx=-[ysin(xy)+1]/[xsin(xy)+1]

①等式两边同对x求导：
y′=1+e^y•y′
y′=1／(1-e^y)
②等式两边同对x求导：
y′=-y′·sin(xy)-1
y′=-1／[1+sin(xy)]

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