两侧对x求偏导得到e^x -ye^z -xye^zdz/dx =0, dz/dx = (e^x-ye^x)/xye^z对y求偏导e^y -xe^z -xye^zdz/dy =0, dz/dy = (e^y-xe^z)/xye^zdz = (dz/dx)dx +(dz/dy)dy= (e^x-ye^x)/xye^z dx +(e^y-xe^z)/xye^z dy
