2.58

;2.56求导
(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 (exponent exp)
                       (make-product (make-exponentiation (base exp) 
                                                          (- (exponent exp) 1))
                                     (deriv (base exp) var))))
        (else
         (display "unknown expression type --DERIV" ))))

;variable?
(define (variable? x) (symbol? x))

;same-variable?
(define (same-variable? x y) (and (symbol? x) (symbol? y) (eq? x y)))

;make-sum
(define (make-sum x y)
  (cond ((= 0 x) y)
        ((= 0 y) x)
        ((and (number? x) (number? y)) (+ x y))
        (else (cons x (cons '+ y)))))

;make-product
(define (make-product x y)
  (cond ((or (= 0 x) (= 0 y)) 0)
        ((= 1 x) y)
        ((= 1 y) x)
        ((and (number? x) (number? y)) (* x y))
        (else (cons x (cons '* y)))))

;=number?
(define (=number? x y) (and (number? x) (number? y) (= x y)))

;sum?
(define (sum? x)
  (and (pair? x) (eq? (cadr x) '+)))

;addend 被加数 表示和式的第二个参数
(define (addend s) (car s))

;augend 加数 表示和式的第三个参数
(define (augend s) 
  (if (null? (cdddr s))
      (caddr s)
      (cons '+ (cddr s))))
;product?
(define (product? x)
  (and (pair? x) (eq? (cadr x) '*)))

;multiplier 被乘数是乘式第二个参数
(define (multiplier p) (car p))

;multiplicand 乘数是乘式里面的第三个参数
(define (multiplicand p) 
  (if (null? (cdddr p))
      (caddr p)
      (cons '* (cddr p))))

;exponentiation?
(define (exponentiation? x)
  (and (pair? x) (eq? (car x) '**)))

;make-exponentiation
(define (make-exponentiation base exponet)
  (cond ((=number? exponet 0) 1)
        ((=number? exponet 1) base)
        ((=number? base 0) 0)
        ((=number? base 1) 1)
        (else (list '** base exponet))))

;base?
(define (base x)
  (cadr x))

;exponet?
(define (exponent x)
  (caddr x))