Perhaps it's a newbie question.., as you can see in this wikipedia animation

Phase velocity (red) and group velocity (green) are described

http://upload.wikimedia.org/wikipedia/commons/b/bd/Wave_group.gif

( * sorry, new users aren't allowed to use image tags)

both show "speed" in the Propagation direction

but

How I calculate the rise speed of a cicle ~~red point~~ in transversal direction?

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?

Thanks for any advice

**EDIT:**

I want to know the up-down axis speed of the wave, watching at the left side of the animation, you can see "first" left most pixel going up and down, this is the vertical speed I want to really calculate