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#lang racket
(define (variable? x) (symbol? x))
(define (same-variable? x y) (and (variable? x) (variable? y) (eq? x y)))
(define (=number? x num)
(and (number? x) (= x num)))
(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 (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 (make-exponent e p)
(cond ((=number? p 0) 1)
((=number? p 1) e)
(else (list '** e p))))
(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))
(define (exponent? x)
(and (pair? x) (eq? (car x) '**)))
(define (base expo)
(cadr expo))
(define (exponent expo)
(caddr expo))
(define e '(+ a b))
(define v1 'a)
(define v2 'b)
(define m1 'a)
(define m2 'b)
(define a1 'a)
(define a2 'b)
(variable? e)
(same-variable? v1 v2)
(sum? e)
(addend e)
(augend e)
(make-sum a1 a2)
(product? e)
(multiplier e)
(multiplicand e)
(make-product m1 m2)
(define (deriv expr var)
(cond ((number? expr) 0)
((variable? expr)
(if (same-variable? expr var) 1 0))
((sum? expr)
(make-sum (deriv (addend expr) var)
(deriv (augend expr) var)))
((product? expr)
(make-sum
(make-product
(multiplier expr)
(deriv (multiplicand expr) var))
(make-product
(deriv (multiplier expr) var)
(multiplicand expr))))
((exponent? expr)
(make-product
(deriv (base expr) var)
(make-product
(exponent expr)
(make-exponent (base expr) (- (exponent expr) 1)))))
(else
(error "unkown expression type -- DERIV" expr))))
(deriv '(+ x 3) 'x)
(deriv '(* x y) 'x)
(deriv '(* (* x y) (+ x 3)) 'x)
(deriv '(** (* 10 a) 3) 'a)
(deriv '(** a 2) 'a)
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