미분 규칙은 표현식 트리를 새 트리로 바꾼다.

(begin
  (define (=number? expression number)
    (and (number? expression) (= expression number)))
  (define (make-sum left right)
    (cond ((=number? left 0) right)
          ((=number? right 0) left)
          ((and (number? left) (number? right)) (+ left right))
          (else (list '+ left right))))
  (define (make-product left right)
    (cond ((or (=number? left 0) (=number? right 0)) 0)
          ((=number? left 1) right)
          ((=number? right 1) left)
          ((and (number? left) (number? right)) (* left right))
          (else (list '* left right))))
  (define (deriv expression variable)
    (cond ((number? expression) 0)
          ((symbol? expression)
           (if (eq? expression variable) 1 0))
          ((eq? (car expression) '+)
           (make-sum (deriv (cadr expression) variable)
                     (deriv (caddr expression) variable)))
          ((eq? (car expression) '*)
           (make-sum
             (make-product (cadr expression)
                           (deriv (caddr expression) variable))
             (make-product (deriv (cadr expression) variable)
                           (caddr expression))))))
  (deriv '(* x (+ x 3)) 'x))