Dear Mitja,

sure, that's quite straight forward. Unfortunately, you did not provide the actual time series so I generated one that might be similar:

tocke = Table[{x, 7655.48 - 1.37747*10^-16 x - 0.0000580449 x^2 + 1.0626*10^-23 x^3 - 8.35914*10^-13 x^4 + 
     1000 RandomVariate[NormalDistribution[]]}, {x, 0, 10000, 100}];

You already fitted a function to that:

funkcija = Fit[tocke, {1, x, x^2, x^3, x^4}, x]

If you want a derivative you can try:

derfunkcija = D[Fit[tocke, {1, x, x^2, x^3, x^4}, x], x]

If you want you can evaluate that at all the points of the original time series.

Table[D[Fit[tocke, {1, x, x^2, x^3, x^4}, x], x] /. x -> xs, {xs, 0, 10000, 100}]

If you prefer taking the x-coordinates directly from the data file you can try this:

D[Fit[tocke, {1, x, x^2, x^3, x^4}, x], x] /. x -> # & /@ tocke[[All, 1]]

Cheers, Marco