As you can see in this wikipedia animation

Phase velocity (red) and group velocity (green) are described, and both show different "speed" in the Propagation direction but what about the transverse direction speed?

How do I calculate the rise speed of a cycle in transversal direction ?

(Look at the extremes of the picture the blue pixel going up and down, this is the vertical up-down speed what I want to calculate)

For example in a very simple wave like this

y(x,t) = A* sin(kx - w t), should I calculate derivative of y having x=constant?

What about in general? How to calculate the Rise speed?