已知y=sin(xy),求其导数.

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已知y=sin(xy),求其导数.已知y=sin(xy),求其导数.已知y=sin(xy),求其导数.解:由复合函数求导可得:Y''=COS(XY)*(XY)''=COS(XY)*(Y+Y''X)把Y=SI

已知y=sin(xy),求其导数.
已知y=sin(xy),求其导数.

已知y=sin(xy),求其导数.
解:
由复合函数求导可得:
Y'=COS(XY)*(XY)'
=COS(XY)*(Y+Y'X)
把Y=SIN(XY)代入上式可得:
Y'=(sin(xy)*cos(xy))/(1-x*cos(xy)) .

（1）
两边对x求导：
y'=cos(xy)*(xy)'
=cos(xy)(y+y'x)
=ycos(xy)+xcos(xy)y'
(1-xcos(xy))y'=ycos(xy)
y'=ycos（xy)/(1-xcos(xy))
(2）隐函数求导：
F(x)=y-sin(xy)
f(x)'=-Fx(x,y)/Fy(x,y)
Fx(x,y)=-ycos(xy)
Fy(x,y)=1-xcos(xy)
所以
f(x)'=ycos(xy)/[1-xcos(xy)]

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