设xy+㏑y+㏑x=1,求dy⼀dx∣x=1

要步骤,步骤
2025-05-22 02:29:40
推荐回答(1个)
回答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