设z=z(x,y)是由方程e^(-xy)+2z-e^z=2确定 求dz|(x=2,y=-1/2)
问题描述：
设z=z(x,y)是由方程e^(-xy)+2z-e^z=2确定 求dz|(x=2,y=-1/2)
答
对方程e^(-xy)+2z-e^z=2两边微分,有：e^(-xy)*d(-xy) + 2*dz - e^z*dz = 0-e^(-xy)*(x*dy + y*dx) + 2*dz - e^z*dz = 0移项,得：(e^z - 2)*dz = -y*e^(-xy)*dx - x*e^(-xy)*dy当x=2,y=-1/2时,代入e^(-xy)+2z-e^z=2,...