Resource > SICP Exersise 2_56
Exersise 2.56
Exersise 2.56
(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))))
((exponentation? exp)
(make-product
(make-product (exponent exp)
(make-exponentiation (base exp) (- (exponent exp) 1)))
(deriv base var)))
(else
(error "unknown expression type -- DERIV" exp))))
(define (exponentiation? exp)
(and (pair? x) (eq? (car x) '**)))
(define (base exp)
(cadr exp))
(define (exponent exp)
(caddr exp))
(define (make-exponentiation base exponent)
(cond [(eq? base 1) 1]
[(eq? exponent 0) 1]
[else (list '** base exponent)]))