求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx

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求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx
求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx

求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx
y'=(y+xy')/(xy)
xyy'-xy'=y
y'=y/(xy-x)
所以dy/dx=y'=y/(xy-x)

y=ln(xy)y'=1/xy*(xy)'=1/xy*(y+xy')
xyy'=y+xy'
xyy'-xy'=y
y'=y/(xy-x)

dy/dx=y/(xy-x)