Ex-2.73

a:
We moved from dispatch on type way of programming to data directed programming that helps bring modularity into the program that is it makes easier to change one part of the program independent of the others. We can't put number, variable into same data directed dispatch as they really don't have type tags and can't be put in operation-type table.

b:

(define (deriv-sum exp)
  (make-sum (deriv (addend exp) var)
            (deriv (augend exp) var)))
(define (deriv-product exp)
  (make-sum
   (make-product (multiplier exp)
                 (deriv (multiplicand exp) var))
   (make-product (deriv (multiplier exp) var)
                 (multiplicand exp))))
;aux code to put them in table
(put 'deriv '(+) deriv-sum)
(put 'deriv '(*) deriv-product)

c:

(define (deriv-exponent exp)
  (make-product
   (exponent exp)
   (make-product
    (make-exponentiation (base exp)
                         (- (exponent exp) 1))
    (deriv (base exp) var))))
(put 'deriv '(**) deriv-exponent) 

d: none