Time differentiation in Pandas

It most certainly does. First, you'll need to convert your indices into pandas date_rangeformat and then use the custom offset functions available to series/dataframes indexed with that class. Helpful documentation here. Read more here about offset aliases.

This code should resample your data to 2.5s intervals

#df is your dataframe
index = pd.date_range(df['time_stamp'])
values = pd.Series(df.values, index=index)

#Read above link about the different Offset Aliases, S=Seconds
resampled_values = values.resample('2.5S') 

resampled_values.diff() #compute the difference between each point!

That should do it.

If you really want the time derivative, then you also need to divide by the time difference (delta time, dt) since last sample

An example:

dti = pd.DatetimeIndex([
    '2018-01-01 00:00:00',
    '2018-01-01 00:00:02',
    '2018-01-01 00:00:03'])

X = pd.DataFrame({'data': [1,3,4]}, index=dti)

X.head()
                    data
2018-01-01 00:00:00 1
2018-01-01 00:00:02 3
2018-01-01 00:00:03 4

You can find the time delta by using the diff() on the DatetimeIndex. This gives you a series of type Time Deltas. You only need the values in seconds, though

dt = pd.Series(df.index).diff().dt.seconds.values

dXdt = df.diff().div(dt, axis=0, )

dXdt.head()
                    data
2018-01-01 00:00:00 NaN
2018-01-01 00:00:02 1.0
2018-01-01 00:00:03 1.0

As you can see, this approach takes into account that there are two seconds between the first two values, and only one between the two last values. :)