Rate of change is nothing more than the number of units that have changed divided by the time it took the change to occur. Yes, you can use an oscilloscope to measure that. For instance, the slew rate of an amplifier (how fast will the output change with a step change at the input) is a typical rate of change specification. Connect the scope to the output, a square wave generator to the input, look at the output on the scope (it will appear as a ramp, depending upon the sweep speed) and for a determined voltage change, say four divisions at 2 volts/div setting for 8 volts, measure the time from those same two points. Divide the voltage by the time to get the units in volts/second.
Dean