Taking derivatives of a curve

A vector valued map like r(t) = ( cos(t+sin(t)),sin(t+sin(t)) ) can be differentiated and define new curves like r'(t). What happens if we plot them? Here is some Mathematica code exploring this: 
r={Cos[s + Sin[s]],Sin[s+Sin[s]]};
F[n_]:=ParametricPlot[D[r,{s,n}] /. s -> t,{t,0,2 Pi}];
GraphicsGrid[Partition[Table[F[n], {n, 1, 6}], 3]]


Here is a prettier picture where the curves are drawn in space: