This calculation amplifies any noise present in the values of the function, often to the point of the output being unusable. There are many methods that can be used to approximate derivatives, depending on the problem. Just as we shouldn't try to invent our cryptographic methods from scratch, we should take advantage of the extensive knowledge already in use for numeric methods.
I've seen naive numeric methods cause everything from jerky motion in video games to incorrect navigation data for cars.
I've seen naive numeric methods cause everything from jerky motion in video games to incorrect navigation data for cars.