You're trying too hard to make up fake reasons to use calculus.
Any self-respecting CS theorist would tell you that accurate progress bars are generally impossible to make because that would reduce to some version of the halting problem; and any self-respecting software engineer would tell you that even in the simple cases where the halting problem is not a problem (eg. simple copying of files), in practice many things outside of the software's control could stall the progress.
Even if you could get an accurate progress value, you don't need a "gradient" to animate it. Just update the bar with the current value as a percentage at 60FPS and you're already done. (Progress bars generally ask the programmer to supply the current progress value, not a stream of progress rates in real time) If you tried to predict the progress "gradient" past the present point, you'd end up having to "lie" (more progress than actual) or have the progress bar jump back when it turns out the actual progress was slower than predicted.
If all you had was a hammer, everything looks like a nail. That almost always applies for those enamored with advanced maths.