Extracting frequency derivative from STFT

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I have a signal that oscillates on short timescales and changes frequency of that oscillation on larger scales. If I do a Short Time Fourier Transform(STFT) or a constant Q transform, I get a feature in frequency space that moves in time. See for example the 2nd row plot of the measurement of gravitational waves.

Ligo detection of gravitational waves - sept 2017

I am interested in the time derivative of f, an estimate of $\dot{f}$. If I have a distribution of f at each timestep, is there a method or algorithm to get a distribution of $\dot{f} (f)$ at each timestep?

Thanks and Best,

Niklas