求隐函数导数ln(xy)=e^x+y所确定的隐函数y=y(x)的导数dy/dx.

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求隐函数导数ln(xy)=e^x+y所确定的隐函数y=y(x)的导数dy/dx.
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求隐函数导数ln(xy)=e^x+y所确定的隐函数y=y(x)的导数dy/dx.
求隐函数导数ln(xy)=e^x+y所确定的隐函数y=y(x)的导数dy/dx.

求隐函数导数ln(xy)=e^x+y所确定的隐函数y=y(x)的导数dy/dx.
ln(xy)=e^x+y
lnx+lny=e^x+y
两边同时对x求导
1/x+(1/y)(dy/dx)=e^x+dy/dx
dy/dx=[(1/x)-e^x]/[1-(1/y)]
=(y-xye^x)/(xy-x)