Using these, and the primitive predicate number?, which identifies numbers, we can express the differentiation rules as the following procedure:
(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))))
(else (error "unknown expression type: DERIV" exp))))[...]
Using these, and the primitive predicate is_number, which identifies numbers, we can express the differentiation rules as the following function:
function deriv(exp, variable) {
return is_number(exp)
? 0
: is_variable(exp)
? is_same_variable(exp, variable) ? 1 : 0
: is_sum(exp)
? make_sum(deriv(addend(exp), variable),
deriv(augend(exp), variable))
: is_product(exp)
? make_sum(make_product(multiplier(exp),
deriv(multiplicand(exp),
variable)),
make_product(deriv(multiplier(exp),
variable),
multiplicand(exp)))
: error(exp, "unknown expression type -- deriv");
}