I have a graph of data, say temperature ($T$) vs time($t$), I know the error bounds in each $\Delta T$.
The range of t is from 0 $\to$ 1600 s, with small steps say 0.001 s.
If I numerically take the derivative at some point on the graph, what is the error associated with that value.
The data is not suitable to be fit with a function or curve.