Examples

  f[x_,y_,z_]:={2 x y,x y z^2-Sin[y z],z Exp[x+y]}
  g[x_,y_]:={x^2 y,Sin[3 x^3 y]}
  h[x_,y_,z_]:={Cos[x y z],Sin[x y z],Exp[x y]}

  div3[f][x,y,z]

  div3[f][x,y,z]/.{x->0,y->0,z->0}

  curl3[f][x,y,z]

  div2[g][x,y]

  curl2[g][x,y]

  div3[h][x,y,z]

  Clear[a,b,c]

  div3[h][a,b,c]

  curl3[h][x,y,z]

Up to Divergence and Curl