2.57.rkt

#lang racket
(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))))
       ((exponentitation? exp)
        (make-product
                     (make-product(exponent exp)
                                  (make-exponentitation (base exp)(-(exponent exp)1)))
                     (deriv (base exp) var)))
      (else
        (error"unkown expression type -- DERIV" exp))))
(define(variable? x)(symbol? x))
(define(same-variable? v1 v2)
  (and(variable? v1)(variable? v2)(eq? v1 v2)))
(define (make-sum a1 a2) 
    (cond((=number? a1 0) a2)
         ((=number? a2 0) a1)
         ((and(number? a1)(number? a2))(+ a1 a2))
         ((sum? a2)(cons '+(cons a1 (cdr a2))))
         (else(list '+ a1 a2))))
(define(=number? exp num)
  (and(number? exp)(= exp num)))

(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))
        ((product? m2)(cons '* (cons m1 (cdr m2))))
         (else(list '* m1 m2))))
(define (sum? x)
  (and (pair? x)(eq? (car x) '+)))
(define(addend s)(cadr s))
(define(augend s)(if(null? (cdddr s))(caddr s)(cons '+ (cddr s))))
(define(product? x)
  (and(pair? x)(eq?(car x) '*)))
(define (multiplier p)(cadr p))
(define(multiplicand p)(if(null? (cdddr p))(caddr p)(cons '* (cddr p))))

;;求幂导数
(define(exponentitation? x)
  (and(pair? x)(eq? (car x) '**)))
(define(base x)
  (cadr x))
(define(exponent x)
  (caddr x))
(define(make-exponentitation b e)
  (cond((=number? e 0)1)
       ((=number? e 1)b)
       (else(list '** b e))))