This rudimentary numerical differentiation script, although very basic, is very useful. It is a Jupyter Notebook
and consists of one function, defined as
As is to be expected, considering the methodology used involves approximation, using more datapoints leads to a higher resolution of estimated
derivatives. The script uses the method of finite differences between points in each array, which is aptly described in
this Wikipedia article.
The script has many uses in my labs work, among other things; for example, where the electric field of a point charge is given by the directional derivative of a given potential, the script can evaluate the electric field's magnitude for a given potential dataset. This is just one example. It may not have many uses to the general user, but is worth having in various circumstances.