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For on-topic questions involving the mathematical concept of a derivative, i.e. $\frac{d}{dx} f(x)$. For purely mathematical questions about the derivative it is better to ask on math SE https://math.stackexchange.com/
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Gradient vs differences to remove non-stationarity in time series?
In theory, the first derivative (similar to what is obtained when computing the gradient using central differences) should also remove any underlying trends in the time series. …