设u=f(x,y,z)具有连续的二阶偏导数，且z=(x,y)由方程xe^x-ye^y=ze^z所确定求du

Answer 1

du = ∂f/∂x dx + ∂f/∂y dy + ∂f/∂z dz..............(1)
dz = ∂z/∂x dx + ∂z/∂y dy...........................(2)
将(2)代入(1):
du = [∂f/∂x + (1+x)/(1+z)e^(x-z)]dx +
+ [∂f/∂y + (1+y)/(1+z)e^(y-z)]dy.......(3)