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

题目

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

答案

x-y+ 1/2 siny=0F(x,y)=y-x-1/2siny=0F,Fx,Fy在定义域的任意点都是连续的,F(0,0)=0Fy(x,y)>0f'(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']...