#lang racket
Ex 2.57
(define (=number? exp num)
  (and (number? exp) (= exp num)))

(define (variable? e)
  (symbol? e))

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

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

(define (addend e)
  (cadr e))

(define (augend e)
  (foldr make-sum 0 (cddr e)))
            
(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 (product? e)
  (and (pair? e) (eq? (car e) '*)))

(define (multiplier e)
  (cadr e))

(define (multiplicand e)
  (foldr make-sum 0 (cddr e)))

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

(define (base e)
  (cadr e))

(define (exponent e)
  (caddr e))

(define (make-exponentiation b e)
  (cond ((=number? b 0) 0)
        ((=number? e 1) b)
        ((=number? e 0) 1)
        ((and (number? b) (number? e)) (expt b e))
        (else (list '** b e))))

(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))))

;; Derivative

(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)
                                                          (make-sum (exponent exp) -1))
                                     (deriv (base exp) var))))
        (else
         (error "Unknown expression type " exp))))




(deriv '(* x x (+ x 3)) 'x)
(deriv '(+ x x (+ x 3)) 'x)
 Derivative
#lang racket
Ex 2.57
(define (=number? exp num)
  (and (number? exp) (= exp num)))

(define (variable? e)
  (symbol? e))

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

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

(define (addend e)
  (cadr e))

(define (augend e)
  (foldr make-sum 0 (cddr e)))
            
(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 (product? e)
  (and (pair? e) (eq? (car e) '*)))

(define (multiplier e)
  (cadr e))

(define (multiplicand e)
  (foldr make-sum 0 (cddr e)))

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

(define (base e)
  (cadr e))

(define (exponent e)
  (caddr e))

(define (make-exponentiation b e)
  (cond ((=number? b 0) 0)
        ((=number? e 1) b)
        ((=number? e 0) 1)
        ((and (number? b) (number? e)) (expt b e))
        (else (list '** b e))))

(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 (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)
                                                          (make-sum (exponent exp) -1))
                                     (deriv (base exp) var))))
        (else
         (error "Unknown expression type " exp))))




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