偏导数数学题设z=(x,y) 是由z+e^z=xy所确定的二元函数,求σ2z/σxσy
2019-05-07
偏导数数学题
设z=(x,y) 是由z+e^z=xy所确定的二元函数,求σ2z/σxσy
优质解答
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
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