(define (make-list n el)
  (cond
    ((= n 0) '())
    ((= n 1) (list el))
    (else (cons el (make-list (- n 1) el)))))

(define (mul-diff-term term sym)
  (if (= (cadr term) (caddr term))
      (diff (car term) sym)
      (car term)))

(define (range i j)
  (if (= i j)
      (list i)
      (cons i (range (+ i 1) j))))

(define (zip as bs cs)
  (map list as bs cs))

(define (gen-mul-terms terms)
  (map (lambda (t) (zip terms (make-list (length terms) t) (range 1 (length terms)))) (range 1 (length terms))))



(define (diff expr sym)
  (if (not (list? expr))
      (if (eq? expr sym)
          1
          0)
      (let ((op (car expr))
            (args (cdr expr)))

           (cond
             ((eq? op '+) (cons '+ (map (lambda (f) (diff f sym)) args)))
             ((eq? op '*) (cons '+ (map (lambda (terms) (cons '* (map (lambda (term) (mul-diff-term term sym)) terms))) (gen-mul-terms args))))
             (else '?))))
  )
;(cons '+ (map (lambda (t) (cons '* (map (lambda (s) (mul-diff-term s 'x)) t))) (gen-mul-list '(x x y))))