Numdifftools

The numdifftools library is a suite of tools written in Python to solve automatic numerical differentiation problems in one or more variables. It employs finite differences in an adaptive manner, coupled with a Richardson extrapolation methodology, to provide maximally accurate results. The library is currently at version 0.9.42 and sees active, though not rapid, development, with the documentation for 0.9.41 updated in late 2025 and PyPI showing an update for 0.9.42 in early 2022.