(define (exponentiation? x)
  (and (pair? x) (eq? (car x) '^)))

(define (base e) (cadr e))
(define (exponent e) (caddr e))

(define (make-exponentiation base exponent)
  (cond ((=number? exponent 0) 1)
        ((=number? exponent 1) base)
        ((and (number? base) (number? exponent)) (expt base exponent))
        (else (list '^ base exponent))))
        
(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)
     (make-product
       (make-product (exponent exp)
                     (make-exponentiation
                       (base exp)
                       (make-sum (exponent exp) -1)))
      (deriv (base exp) var)))
    (else
     (error "unknown expression type -- DERIV" exp))
))