这不是二重积分,是隐函数的二阶偏导数……
设F(x,y,z)=z+e^z-xy
则Fx=-y,Fy=-x,Fz=1+e^z
αz/αx=-Fx/Fz=y/(1+e^z),αz/αy=-Fy/Fz=x/(1+e^z)
σ²z/σxσy=α(αz/αx)/αy=-y/(1+e^z)^2*(αz/αy)
=-xy/(1+e^z)^3
这不是二重积分,是隐函数的二阶偏导数……
设F(x,y,z)=z+e^z-xy
则Fx=-y,Fy=-x,Fz=1+e^z
αz/αx=-Fx/Fz=y/(1+e^z),αz/αy=-Fy/Fz=x/(1+e^z)
σ²z/σxσy=α(αz/αx)/αy=-y/(1+e^z)^2*(αz/αy)
=-xy/(1+e^z)^3