(define (compose f g)
  (lambda (x) (f(g x))))

(define (derive f dx)
  (lambda (x)
    (/(-(f(+ x dx)) (f x)) dx)))

(define (square x) (* x x))
(define (cube x) (* x x x))

(define (repeated f N)
  (cond ((= n 0) (lambda(x) x))
        ((= n 1) f)
        (else (compose f
                       (repeated f (- N 1))))))

(define (id1 x) 1)
(define (square1 x)(* 2 x))
(define (qube1 x) (* 3 x x))





(define (compare f g x)
  (display "(f x) = ")
  (display (f x))
  (display " (g x)")
  (display (g x))
  (display " compare: ")
  (display (= (f x) (g x)))
  (display " difference: ")
  (display (- (f x)(g x)))
  (display "\n"))


(define (compare1 f g x)
  (let (
        (valueF (f x))
        (valueG (g x))
        )
    (diaplay " (f x) = ")(display (valueF))
    (diaplay " (g x) = ")(display (valueG))
    (display " compare: ")(display (= valueF valueG))
    (display " difference: ")(display (- valueF valueG))))


(define (cube2 x) (* 6 x))
(define (cube3 x) 6)
(define (id x) x)

(define (compare-interval f g a b)
  (if (> a b) (display "End.\n")
      (begin (compare f g a)
             (compare-interval f g (+ a 1) b))))

(display "Comparing id and id1:\n")

(compare-interval (derive id 0.00001) id1 1 10)

(compare (derive square 0.00001) square1 1.99999999999)

(define (deriveN f N dx)
    ((repeated (lambda(f) derive f dx) N) f)
  )

(compare-interval (deriveN cube 2 0.00001) cube2 1 10)