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;; From the book, extended
(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 (variable? x) (symbol? x))
(define (same-variable? v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(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 (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 (=number? exp num)
(and (number? exp) (= exp num)))
(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))))
;; Added procedures for differentiating variables raised to powers
(define (exponentiation? x)
(and (pair? x) (eq? (car x) '**)))
(define (base p) (cadr p))
(define (exponent p) (caddr p))
(define (make-exponentiation base exponent)
(cond ((=number? exponent 0) 1)
((=number? exponent 1) base)
((and (number? base) (number? exponent)) (** base exponent))
(else (list '** base exponent))))
(define ** expt)
;; Tests
(deriv '(** x 4) 'x) ; '(* 4 (** x 3))
(deriv '(+ (** x 3) (* 5 x)) 'x) ; '(+ (* 3 (** x 2)) 5)
(deriv '(+ 3 x x 4 7) 'x) ; 1 (can't handle sums with more than 2 arguments)