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;; This buffer is for notes you don't want to save, and for Lisp evaluation.
;; If you want to create a file, visit that file with C-x C-f,
;; then enter the text in that file's own buffer.
(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
(make-product (exponent exp)
(make-exponentiation (base exp)
(- (exponent exp) 1)))
(deriv (base exp) var)))
(else
(error "unknown expression type -- DERIV" exp))))
(define (binary-expression? x)
(eq? (cdddr x) '()))
(define (=number? exp num)
(and (number? exp) (= exp num)))
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2) (eq? v1 v2))
(define (make-sum a1 a2)
(cond ((null? a2) a1)
((=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-exponentiation b e)
(cond ((=number? e 0) 1)
((=number? e 1) b)
(else (list b '** e))))
(define (addend s) (car s))
(define (augend s) (caddr s))
(define (sum? x)
(and (pair? x) (eq? (cadr x) '+)))
(define (product? x)
(and (pair? x) (eq? (cadr x) '*)))
(define (multiplier p) (car p))
(define (multiplicand p) (caddr p))
(define (base e) (car e))
(define (exponent e) (caddr e))
(define (exponentiation? e)
(and (pair? e) (eq? (cadr e) '**)))
(deriv '(x + (3 * (x + (y + 2)))) 'x)
(deriv '((x * y) * (x + 3)) 'x)
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