plot derivative; plot with points

Hi all.

I have two different queries on Gnuplot features:
(1) Is it possible to plot derivative of a data file? In other words,
if I have a data file that gives y-data as a function of x-data, can I
plot dy/dx in Gnuplot from the data file?
(2) I have a data file with many data points. I plot it 'with points'
option. The problem is that where the curve is flat (horizontal), the
points are too much dense, giving a thick-line like look, and where
the curve is steep, the points look rarer and the plot is ok. If I use
the 'every' option, say 'every 2', then the problem is lessened in the
denser region, but the plot becomes rarer in the already rare region,
and this is not desirable. Is there a way in which I can plot the
curve 'with points' with variable point density in the different parts
or ranges of the plot?
(I use Gnuplot version 4.0)

Thankyou

.

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