求由方程x-y+ 1/2 siny=0所确定的隐函数y的二阶导数d^2y/dx^2答:F(0,0)=0 Fy(x,y)>0 f'(x)=-Fx(x,y)/Fy(x,y)=1/(1-1/2cosy)=2/(2-cosy)Fx(x,y)+Fy(x,y)y'=0 再求导:Fxx(x,y)+Fxy(x,y)y'+[Fyx(x,y)+Fyy(x,y)y']y'+Fy(x,y)y''=0 所以 y''=[2FxFyFxy-F^2yFxx-F^2xFyy]/F^3y 将每一个偏导数分别求出来...
举一个某个二元函数的两个混合二阶偏导数在某一点的值相等但在该点这...答:Fy'(x,y)=3x^3y^2sin(1/(xy))-x^2ycos(1/(xy)).3.xy=0,显然有 Fxy''(x,y)=Fyx''(x,y)=0.4.xy≠0,Fxy''(x,y)=Fyx''(x,y)= =9x^2y^2sin(1/(xy))-5xycos(1/(xy))-sin(1/(xy)).==> 在R^2上,F(x,y)的二阶混合偏导数相等,但是二阶混合偏导数不连续....