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If I have a discrete real-time signal $x[n]$, with its latest value $x[i]$ and all its past values $x[i-t]$, how can I estimate the derivative at $x[i]$?
Is the derivative between x[n] and x[n-1] useful enough, hence x'[n] = x[n] - x[n-1] ? Or do you need a better estimate?
A reasonable solution in this case would be to do a curve fit and then establish an estimate of the derivative using the "smoothed" solution, which would help eliminate your noise issues.
Required, but never shown