Derivative

derivative.scm

(define (menq item sequence)
  (cond ((null? sequence) false)
      ((eq? item (car sequence)) sequence)
      (else (memq item (cdr sequence)))))

(list 'a 'b 'c)

(equal? '(this is a list) '(this is a list))
(equal? '(this is a list) '(this '(is a) list))

; 2.54

(define (append seq1 seq2)
  (if (null? seq1)
      seq2
      (cons (car seq1) (append (cdr seq1) seq2))))

(append '(1 '(2 3)) '(4 5 6))

; 2.56

(define (variable? exp)
  (symbol? exp))

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

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

(define (addend exp)
  (cadr exp))

(define (augend exp)
  (caddr exp))

(define (make-sum a1 a2)
  (list '+ a1 a2))

(define (make-exponentiation b n)
  (cond ((=number? exponent 0) 1)
        ((=number? exponent 1) b)
        (else (list( '^ base exponent))))

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

(define (multiplier exp)
  (cadr exp))

(define (multiplicand exp)
  (caddr exp))

(define (make-product m1 m2)
  (list '* m1 m2))

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

(define (exponentiation? exp)
   (and (pair? exp) (eq? (car exp) '**)))

(define (base exp)
  (cadr exp))

(define (exponent exp)
  (caddr exp))


(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? 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 (exponent exp) 
                        (make-product
                        (make-exponentiation (base exp) (- (exponent exp) 1))
                         (deriv (base exp) var))))
        (else
         (error "unknown expression type——DERIV" exp))))