设xy+㏑y+㏑x=1,求dy/dx∣x=1

设xy+㏑y+㏑x=1,求dy/dx∣x=1
设xy+㏑y+㏑x=1,求dy/dx∣x=1

设xy+㏑y+㏑x=1,求dy/dx∣x=1
d(xy)+d(㏑y)+d(㏑x)=d(1)
y*dx+x*dy+1/y*dy+1/x*dx=0
(x+1/y)dy=(-y-1/x)dx
dy/dx=(-y-1/x)/(x+1/y)
x=1
代入xy+㏑y+㏑x=1
y+㏑y+0=1
y=1
所以dy/dx∣x=1=(-1-1)/(1+1)=-1