2.57.scm

(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))
;;(define (make-sum a1 a2) (list '+ a1 a2))
(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 (=number? exp num)
  (and (number? exp) (= exp num)))

;;(define (make-product m1 m2) (list '* m1 m2))
(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) (caddr s))

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

;;(define (multiplicand p) (caddr p))


(deriv '(+ x 3) 'x)
(deriv '(* x y) 'x)
(deriv '(* (* x y) (+ x 3)) 'x)

(define (exponentiation? exp)
  (and (pair? exp) (eq? (car exp) '**)))
(define (base s) (cadr s))
(define (exponent s) (caddr s))
(define (make-exponentiation b e)
  (cond ((=number? e 0) 1)
        ((=number? e 1) b)
        ((and (number? b) (number? e)) (expt b e))
        (else (list '** b e))))

(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))))
        ((exponentiation? exp)
         (make-product
          (make-product (exponent exp)
                        (make-exponentiation (base exp)
                                             (- (exponent exp) 1)))
          (deriv (base exp) var)))
        (else
         (error "unknown expression type -- DERIV" exp))))

(exponentiation? '(** x 3))
(base '(** x 3))
(exponent '(** x 3))
(make-exponentiation 'x 3)
(deriv '(** x 3) 'x)
(deriv '(** y 3) 'x)
(deriv '(** 3 3) 'x)
;;(deriv '(** x y) 'x) exponent must be the number
(deriv '(** x 0) 'x)
(deriv '(** x 1) 'x)

;;---- ex 2.57 ---------
(define (augend s) 
  (if (null? (cdddr s)) (caddr s)
      (cons '+ (cddr s))))

(define (multiplicand p)
  (if (null? (cdddr p)) (caddr p)
      (cons '* (cddr p))))

(deriv '(+ x y 3) 'x)
(deriv '(+ x (+ x y 3)) 'x)
(deriv '(+ (+ x y) (+ x x (+ y 3))) 'x)

(deriv '(* x y 3) 'x)
(deriv '(* x y (+ x 3)) 'x)