Plotting a Derivative in Scheme

Question

I wrote a derivative function as follows:

(define (der f h)
 (lambda (x)
 (/ (- (f(+ x h)) (f x)) h)))

and another function for finding second and third derivatives :

(define (der-multiple f h n)
 (if (= 0 n)
  0
  (der (f h)))
       (- n 1))

I tried to plot the derivative of sin(x) as follows, but it did not work.

(define (f x) (der (sin x) 0.5))
(require plot)
(plot (function f (- 5) 5 #:label "sine^-1(x)")
  #:x-min -5 #:x-max 5 #:y-min -5 #:y-max 5)

lang racket is imported, but all I am getting is a white screen. Did I do something wrong here? Should I change (lambda (x)) within the derivative function to something else to make the function easier to plot?

Updated Code

(define (der f h)
  (lambda (x)
  (/ (- (f(+ x h)) (f x))
     h)))

(define (der-multiple f h n)
  (if (= 0 n)
      f
      (der-multiple (der f h) h (- n 1))))
(define (der-sin-fourth h)
(der-multiple sin h 4))
(plot (function (der-sin-fourth 0.5) (- 5) 5 #:label "sine^-4(x)")
        :x-min -5 #:x-max 5 #:y-min -5 #:y-max 5)

Answer 1

Your der returns a function of x, which is fine. But your

(define (f x) (der (sin x) 0.5))

has a number of problems. First, since der returns a function, all that f does is return a function - it does no computation on x. Probably you wanted:

(define f (der (sin x) 0.5))

so that f is actually bound to a function of x.

Second, the argument to der is expected to be a function, but with (sin x) you, at best, pass in a number.

In summary, probably you want something like:

(define f (der sin 0.5))

Note, your h of 0.5 is probably too big to get a reasonable derivative (recall sin is periodic outside of {0, 2pi}). You'll have no issues making h very small. Of course, when you plot it you can step x by 0.5 if you want.

Your der-multiple function isn't correct in a number of ways. Here is the proper version:

(define (der-n f h n)
  (if (zero? n)
      f
      (der-n (der f h) h (- n 1))))