求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx
问题描述：
求由隐函数y=ln(xy)所确定的函数y=y(x)的导数dy/dx
答
y=ln(xy)y'=1/xy*(xy)'=1/xy*(y+xy')
xyy'=y+xy'
xyy'-xy'=y
y'=y/(xy-x)
即
dy/dx=y/(xy-x)
答
y'=(y+xy')/(xy)
xyy'-xy'=y
y'=y/(xy-x)
所以dy/dx=y'=y/(xy-x)