Higher order differentials: dZ, d^2Z, d^3Z

[Ask4material]

Any books discussing the formula of $d^2Z$ and $d^3Z$?
Are they liked that? Anyone saw them before?

$Z(x, y)\\\\dZ=Z_xdx+Z_ydy\\d^2Z=Z_{xx}(dx)^2+2Z_{xy}dxdy+Z_{yy}(dy)^2+Z_xd^2x+Z_yd^2y\\d^3Z=Z_{xxx}(dx)^3+3Z{xxy}(dx<br /> )^2(dy)+3Z_{xyy}(dx)(dy)^2+Z_{yyy}(dy)^3+3[Z_{xx}(dx)(d^2x)+Z_{xy}(dxd^2y+d^2xdy)+Z_{yy}(dy)(d^2y)]+Z_xd^3x+Z_yd^3y$

 

[HallsofIvy]

ANY (modern) text on differential geometry and differentials will deal with those.