Then I keep hearing that "the derivative of phase is frequency" but in this context what does "phase" mean?

Have a look at the phasor representation of AC signals, e.g. described

here. The phasor is an arrow with a length (aka amplitude) and an angle to the x-axis. This angle is the phase of the phasor (it's no coincidence the arrow has been dubbed phasor

).

To create a sinusoidal wave, this phasor rotates (typically counter-clockwise) around the origin. The length of the phasor stays the same all the time. The rotation can be describes as a change in angel (phase). The faster the phasor rotates, the more rottaions fit into a given timeslot (e.g. 1 second). The number of rotations per second is therefore the frequency of the sine wave. The number of rotations per second is equivalent to the change in angle (phase) over that time: each rotation adds 2*PI to the phase (you accumulate the phase, you do not re-start at 0 when the phasor corsses the rightward pointing x-axis). Therefore the derivative of the (accumulated) phase with respect to time is equivalent to the frequency.

The possible issue with the term 'phase' here is that it may seem to have different meanings depending on the context. But in reality there is no difference.

One meaning which may be better known to you is the phase between two sines. This is in reality the phase difference. If both sines have the exact same frequency but their zero crossings happen at different points in time, the phase difference is fixed and can be calculated from the frequency and the time difference of the zero crossings.

If both sines have different frequencies, the phase difference changes with time.

You can easily draw this in a simple diagram.

The other meaning of phase is as described above as the angle of a phasor with reference to the x-axis and a fixed point in time where phase is by definition 0 ° (imagine the phasor being at rest and starting to rotate at time T0, then this is the reference point). With each full rotation of the phasor the accumulated phase is increased by 2*PI.

The phase thus can be described as phi1(t) = 2*PI*f*t where T0 = 0, f = frequency, t = time

A second signal with an offset in phase to this first signal can be described as phi2(t) = 2*PI*f*t +delta_phi where delta_phi is the fixed offset in phase.

The phase difference of these two signals is phi2(t)-phi1(t) = (2*PI*f*t +delta_phi) - (2*PI*f*t) = delta_phi as expected.

The derivative of e.g. phi1(t) with respect to time is dphi1(t)/dt = d(2*PI*f*t)/dt = 2*PI*f. This is the

angular frequency of the signal, the 'speed' at which the phasor rotates.

Hope that helps you get along.

By the way: congratulations to your choice of book. I don't know the one on PLLs, but I know 2 other books by Roland Best and I think he's a good author, explaining matters well.