[求助] 大一高等数学求助 已有3人参与

2楼: Originally posted by feixiaolin at 2014-02-07 15:42:58
取F(x, y)=x*y^2 + e^y - cos(x + y^2)
∂F/∂x=sin(x + y^2) +y^2
∂F/∂y=2*x*y + e^y + 2*y*sin(x + y^2)
dy/dx=-(∂F/∂x)/(∂F/∂y)=……
dy=-(∂F/∂ ...

3楼: Originally posted by mathstudy at 2014-02-07 19:19:23
两侧对 变量x 微分 可得:

y^2 dx+ 2xy dy+ e^y dy =-sin(x+y^2)*(dx +2y dy)整理两侧
得出
dy=即可

4楼: Originally posted by peterflyer at 2014-02-07 20:38:44
按照复合函数的求导原则对方程两边对x进行求导或微分:
y^2+2*x*y*y'+e^y*y'=-Sin*
y'={-Sin(x+y^2)-y^2}/{2*x*y+e^y+Sin(x+y^2)}
dy=y'*dx==dx/[2xy+ey+2ysin(x+y2)