The right way to plot f'[x]

Consider several attempts to plot the derivative of f[x] below.

This first attempt doesn't work at all.

The second attempt works, but takes over 11 seconds, because the derivative is derived for every sample point.

The best version is below,and takes a little more than 1 second. It works much faster because the derivative is worked out only once (before the derivative is sampled).

Created by Mathematica (May 16, 2004)