density function

I wonder if the function "density" outputs the gaussian mixture formula that 
is estimated from the input data, assuming a gaussian model is used at each 
data point ?  I want to take the derivative of the finally estimated gaussian 
mixture formula for further analysis.

It is a kernel density estimate: a rather trivial mixture, not necessarily 
Gaussian.  Also, it is not set up to optimally estimate a derivative, and 
you should look at more sophisticated methods in other packages if you 
want to do that.

As to what "density" outputs: see its help page.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595