作业帮xy+㏑ y+㏑ x=0 求dy/dx
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xy+㏑ y+㏑ x=0 求dy/dx
xy+㏑ y+㏑ x=0 求dy/dx
xy+㏑ y+㏑ x=0 求dy/dx
两边同时求导
x+x(dy/dx)+1*(dy/dx)/y+1/x=0
合并同类项 dy/dx=-y/x
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
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