In a language with higher-order procedures like Lisp or Julia, you can write code that actually returns the derivative as a function, as opposed to differentiat

In a language with higher-order procedures like Lisp or Julia, you can write code that actually returns the derivative as a function, as opposed to differentiate at a given point. This is harder to do (gracefully, anyway) in e.g. C. The beauty of the functional approach is that it corresponds much more closely to how we think about math. See for example Structure & Interpretation of Classical Mechanics (http://mitpress.mit.edu/sites/default/files/titles/content/sicm_edition_2/toc.html http://mitpress.mit.edu/sites/default/files/titles/content/s...). This is especially powerful when combined with automatic differentiation, as is done in the ScmUtils system that goes along with SICM. (Finite differencing has numerical stability issues when carried too far.)