Another example which cannot be done with TikZ. The image shows the first 15 derivations off(x)=1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800+x^12/479001600-x^14/87178291200 (black curve),calculated by the PS function Derive:
\documentclass{article}\usepackage[dvipsnames]{pstricks}\usepackage{pstricks-add}\begin{document}\psset{unit=2}\def\getColor#1{% \ifcase#1 black\or RedOrange\or magenta\or yellow\or green\or Orange\or blue\or DarkOrchid\or BrickRed\or Rhodamine\or OliveGreen\or Goldenrod\or Mahogany\or OrangeRed\or CarnationPink\or RoyalPurple\or Lavender\fi}\begin{pspicture}[showgrid](0,-2.2)(8,1.5)\psclip{\psframe[linestyle=none](0,-2)(8,1.1)}\multido{\in=15+-1}{16}{% \ifnum\in=0 \psset{linewidth=1.75pt}\else\psset{linewidth=1pt}\fi% \psplot[algebraic,linecolor=\getColor{\in}]% {0}{7}{Derive(\in, 1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800+x^12/479001600-x^14/87178291200)}}\endpsclip\end{pspicture}\end{document}