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

y'=(y+xy')/(xy)
xyy'-xy'=y
y'=y/(xy-x)
所以dy/dx=y'=y/(xy-x)