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;; Only augend and multiplicand needed modification
(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) ; this
(make-product ; is
(make-product (exponent exp) ; new
(make-exponentiation (base exp) ;
(sub1 (exponent exp)))) ;
(deriv (base exp) var))) ;
(else
(error "unknown expression type - DERIV" exp))))
(define (sum? x)
(and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
;; Extended
(define (augend s)
(if (= (length s) 3)
(caddr s)
(cons '+ (cddr s))))
(define (product? x)
(and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
;; Extended
(define (multiplicand p)
(if (= (length p) 3)
(caddr p)
(cons '* (cddr p))))
(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))))
;; Tests
(deriv '(* x y (+ x 3)) 'x) ; '(+ (* x y) (* y (+ x 3)))
(deriv '(+ (* 4 x) (* 7 (** x 3)) (* x 5)) 'x)
; '(+ 4 (+ (* 7 (* 3 (** x 2))) 5))
(deriv '(* 4 x (** (+ x (* 6 y) 2) 3) z) 'y)
; '(* 4 (* x (* (* (* 3 (** (+ x (* 6 y) 2) 2)) 6) z)))