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画红色笔的, 

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/07/06 00:55:58
画红色笔的,
 
8.d ( xy + ln y = 1 )
ydx + xdy + 1/y * dy = 0
y' = dy/dx = - y^2 / ( xy + 1 )
9.2.d ( xy = e ^(x+y) )
ydx + xdy = e^(x+y) ( dx + dy )
y' = dy/dx = ( y - e ^(x+y) ) / ( e^(x+y) - x )
再问: 大神可否做在纸上给我看看,酱紫看不懂啊
再答: d ( xy + ln y = 1 )
xdy + ydx + 1/y * dy = 0

ydx = - xdy - 1/y dy
ydx = - ( x + 1/y ) dy

两边除以 - ( x + 1/y )
- y / ( x + 1/y ) * dx = dy

两边除以 dx
- y / ( x + 1/y ) = dy/dx

简化
- y^2 / ( xy + 1 ) = dy/dx

y' = dy/dx

所以
y'= dy/dx = - y^2 / ( xy + 1 )