gnuplot - error bars and fitting for calculations from raw data
===

What does gnuplot do if I have a data.txt file like this:

    #x  y  dx  dy
     1  2  0.2 0.1 
     3  5  0.1 0.3

Where the dx and dy are the errors directly related to x and y (x +- dx, y +- dy). And I do this:

    plot data.txt using (1/$1):($2*5):3:4 with xyerrorbars

Will gnuplot do this for x and y

    (1/x) +- dx
    5y +- dy

or that

    1/(x +- dx)
    5(y +- dy)

or that

    1/x +- 1/dx

or that, the Gaussian error propagation, which would be the right one, gotten from the sqrt(sum(derivative times the error)^2)

    1/x -+ dx/x^2

And how to fit in this case?