FiniteDifferences.jl estimates derivatives with finite differences. See also the Python package FDM. FiniteDiff.jl and FiniteDifferences.jl are similar libraries: both calculate approximate derivatives numerically. You should definitely use one or the other, rather than the legacy Calculus.jl finite differencing, or reimplementing it yourself. At some point in the future, they might merge, or one might depend on the other.