设函数y由方程ln y+x/y=0确定,求dy/dx

问题描述:

设函数y由方程ln y+x/y=0确定,求dy/dx

dy/dx*(1/y)+(1/y)+dy/dx*(-x/y2)=0

合并:dy/dx*(y-x)/y2=-1/y;

可得:dy/dx=y/(x-y);

ln y+x/y=0
等式两边求导:
y'*1/y+1/y+x*y'(-1/y²)=0
(1/y-x/y²)y'=-1/y
∴y'=(-1/y)/(1/y-x/y²)=-y/(y-x)
∴dy/dx=-y/(y-x)