The first and second partial derivatives of XYZ = x + y + Z I want to know more about it

The first and second partial derivatives of XYZ = x + y + Z I want to know more about it

xyz=x+y+z
yzdx+xzdy+xydz=dx+dy+dz
xydz-dz=dx-yzdx+dy-xzdy
dz=[1/(xy-1)][(1-yz)dx+(1-xz)dy].