2.57.scm

(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)
         (make-sum (deriv (addend exp) var)
                   (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
          (make-product 
           (multiplier exp)
           (deriv (multiplicand exp) var))
          (make-product 
           (deriv (multiplier exp) var)
           (multiplicand exp))))
        (else (error "unknown expression 
                      type: DERIV" exp))))

(define (variable? x) (symbol? x))

(define (same-variable? v1 v2)
  (and (variable? v1)
       (variable? v2)
       (eq? v1 v2)))

(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) 
         (+ a1 a2))
        (else (list '+ a1 a2))))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) 
             (=number? m2 0)) 
         0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) 
         (* m1 m2))
        (else (list '* m1 m2))))

(define (sum? x)
  (and (pair? x) (eq? (car x) '+)))

(define (addend s) (cadr s))

(define (augend s)
(let ((value (cddr s)))
(if (null? (cdr value)) (car value) (cons (car s) value))))

(define (product? x)
  (and (pair? x) (eq? (car x) '*)))

(define (multiplier p) (cadr p))

(define (multiplicand p)
(let ((value (cddr p)))
(if (null? (cdr value)) (car value) (cons (car p) value))))

(define (=number? exp num)
  (and (number? exp) (= exp num)))