I am sharing some Python code code that I wrote as a school assignment. This computes the Newton form of the interpolation polynomial of a given set of points, and allows for the evaluation of both the polynomial and its derivative, at a given point. This is an accurate way of estimating the derivative of a complicated function.
Initially it plots the function, the interpolating polynomial and its derivative. When clicking on the plot, the tangent to the interpolating polynomial at the horizontal position of the mouse cursor is plotted.
It can be found here: https://gist.github.com/921554