Question

3.设x+y+z=e2确定函数z=f(x,y),求全微分d

Answer 1

d(x+y+z)=d(e^2)=0
dx+dy+dz=0
dz=-(dx+dy)

Answer 2

若是 x+y+z = e^2, z = e^2-x-y， dz = - dx - dy 。
若是 x+y+z = e^z, 两边对 x 求偏导，得
则 1 + ∂z/∂x = e^z∂z/∂x, ∂z/∂x = 1/(e^z-1)
同理， ∂z/∂y = 1/(e^z-1)
dz = (dx + dy)/(e^z-1)