Watts per second, or Joules per second-squared, could be correctly used to describe rate of change of power.
Watts per hour, or Joules per second per hour, could also be used, but it would be confusing.
But rate of change of power is something that almost never comes up, and it's a lame attempt to find a gnat's penis worth of redeeming value in an earlier post that was actually just a mistake.
Another place it might be used is to describe how quickly a powerplant can change its output to match a changing load.