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I've heard that one of McCarthy's original motivations for inventing Lisp was to write a system for automatic differentiation. Despite this, my Google searches haven't yielded any libraries/macros for doing this. Are there any Scheme/Common Lisp/Clojure libraries (macros) out there for taking a function F and returning a function dF/dx that calculates the derivative of F? I would want it to support F's with multiple arguments. The user would choose which of these is the x to differentiate with respect to. Ideally, the differentiator would work even for vector-valued F's and x's. EDIT : Several people have mentioned symbolic differentiation. The difference between symbolic differentiation and automatic differentiation is a subtle one, but it's summarized well in Wikipedia , and particularly in this picture . This distinction isn't as strong in lisp, where symbolic expressions can be turned into working programs as-is, but there remains a potential difficulty: Symbolic differentiation requires the expression being differentiated to be composed of operations with known derivatives. For example, someone mentioned SICP's example of a macro that churns through simple sexps like (+ y (* (x y))) , and uses the chain rule, along with knowledge of how to differentiate + and * , to return a sexp that represents the derivative. I would need that to work with expressions like (* (foo x y) (bar x)) , where foo and bar may in turn call other functions whose derivatives aren't known at differentiation time. This would be fine if there's a way to take an expression like (foo x y) and replace it with its function body, substitu

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