Question

8、求下列函数的全微分dz (1)没函数z= z(x,y)由方程x+y+z=e^z所确定，求dz

Answer 1

解答如图

Answer 2

x+y+z=e^z
dx+dy+dz = e^z dz
(e^z -1) dz = dx+dy
dz = (dx+dy)/(e^z -1)
= (dx+dy)/(x+y+z -1)