;; sicp 2.3 (define (deriv exp var) (cond ((numberp 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)))) (else (error "unknown expression type -- DERIV" exp)))) (define pair? consp) (define (variable? x) (symbolp 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)) ;; these leave us with unsimplified results ;; (define (make-sum a1 a2) (list '+ a1 a2)) ;; (define (make-product m1 m2) (list '* m1 m2)) (define (make-sum a1 a2) (cond ((=number? a1 0) a2) ((=number? a2 0) a1) ((and (numberp a1) (numberp a2)) (+ a1 a2)) (t (list '+ a1 a2)))) (define (=number? exp num) (and (numberp 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 (numberp m1) (numberp m2)) (* m1 m2)) (t (list '* m1 m2)))) ;; (deriv '(* x y) 'x) => y ;; (deriv '(* x x) 'x) => (+ x x) ;; (deriv '(* x (* x x)) 'x) => (+ (* x (+ x x)) (* x x)) = 3x^2 ;; (deriv '(* 2 (* x x)) 'x) => (* 2 (+ x x)) = 4x