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it would be high rate of CHANGE IN position (with respect to time). if you just think about it, saying "rate of position" just sounds weird and doesn't even mean anything. at least IVE never heard a derivative being worded like that by any professor or textbook. saying "rate of" anything to refer to a derivative is just wrong altogether. with that said, if the correct way of referring to velocity is rate of change in position then logically its ok to say rate of speed (since it makes sense to say rate of change). so really saying the OF in the phrase "rate of speed" is simply to indicate what kind of rate is being referred to. if i say the car was traveling at a high rate, one could ask "rate of what?" ...rate of speed. in conclusion, no derivative was ever implied and is simply a phrase made by reporters or whoever to sound smart but the phrase itself is not technically wrong.
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