函数z+z(x,y)由方程F(x+y,x+z)=1所确定,其中F有二阶连续偏导数,且F2不等于0,求∂^2z/∂y^2
问题描述:
函数z+z(x,y)由方程F(x+y,x+z)=1所确定,其中F有二阶连续偏导数,且F2不等于0,求∂^2z/∂y^2
答
F(x+y,x+z)=1F1+F2(∂z/∂y)=0 ∂z/∂y= -F1/F2∂²z/∂y²=[-F2(F11+F12(∂z/∂y))+F1(F21+F22(∂z/∂y)]/F2^2=[-F2(F11+F12(-F1/F2))+F1(F21+F22(-F1/...