qwertyuiop
Most modern jets use IRU's which incorporate 3 RATE gyro's. Yaw rate being fed from these.
Several Yaw dampers on older a/c had a built in rate gyro, others used derived rate fed from a basic DG.
However damping of dutch roll (can we still say that in these overly PC times??) is, and will always be, a rate function. It is what is known as a rate/rate system i.e. system response is a product of the RATE of displacement rather than size of the displacement.