diff --git a/ex-2_53-xx.scm b/ex-2_53-xx.scm
index e69de29..e2500df 100644
--- a/ex-2_53-xx.scm
+++ b/ex-2_53-xx.scm
@@ -0,0 +1,113 @@
+(load "util.scm")
+
+(define (memq item x)
+  (cond ((null? x) false)
+        ((eq? item (car x)) x)
+        (else (memq item (cdr x)))))
+
+(display "ex-2.53 - symbols (see comments)") (newline)
+
+(list 'a 'b 'c)                         ; (a b c)
+(list (list 'george))                   ; ((george))
+(cdr '((x1 x2) (y1 y2)))                ; ((y1 y2))
+(cadr '((x1 x2) (y1 y2)))               ; (y1 y2)
+(pair? (car '(a short list)))           ; #f
+(memq 'red '((red shoes) (blue socks))) ; #f
+(memq 'red '(red shoes blue socks))     ; (red shoes blue socks)
+(newline)
+
+(display "ex-2.54 - equal?") (newline)
+
+(define (my-equal? a b)
+  (cond
+    ((and (null? a) (null? b)) #t)
+    ((eq? (car a) (car b)) (my-equal? (cdr a) (cdr b)))
+    (else #f)))
+
+(assert (my-equal? '(this is a list) '(this is a list)) #t)
+(assert (my-equal? '(this is a list) '(this (is a) list)) #f)
+(newline)
+
+(display "ex-2.55 - double quote") (newline)
+
+; The expression after car yields `(quote abracadabra)`. Consequently car
+; returns `quote`.
+(display (car ''abracadabra))
+
+(newline) (newline)
+(display "example - symbolic differentiation\n")
+
+(define (variable? x) (symbol? x))
+(define (same-variable? v1 v2)
+  (and (variable? v1) (variable? v2) (eq? v1 v2)))
+(define (=number? exp num)
+  (and (number? exp) (= exp num)))
+(define (make-sum a1 a2)
+  (cond ((=number? a1 0) a2)
+        ((=number? a2 0) a1)
+        ((and (number? a1) (number? a2)) (+ a1 a2))
+        (else (list '+ a1 a2))))
+(define (make-product m1 m2)
+  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
+        ((=number? m1 1) m2)
+        ((=number? m2 1) m1)
+        ((and (number? m1) (number? m2)) (* m1 m2))
+        (else (list '* m1 m2))))
+
+(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 cadr)
+(define multiplicand caddr)
+
+(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)
+         (let ((b (base exp))
+               (e (exponent exp)))
+           (make-product
+             (make-product e (make-exponentiation b (make-sum e -1)))
+             (deriv b var))))
+        (else
+         (error "unknown expression type -- DERIV" exp))))
+
+(display (deriv '(+ x 3) 'x)) (newline) ; (+ 1 0)
+(display (deriv '(* x y) 'x)) (newline) ; (+ (* x 0) (* 1 y))
+(display (deriv '(* (* x y) (+ x 3)) 'x))
+;(+ (* (* x y) (+ 1 0))
+;   (* (+ (* x 0) (* 1 y))
+;      (+  x 3)))
+
+
+(display "\n\nex-2.56\n")
+
+(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
+(define base cadr)
+(define exponent caddr)
+(define (make-exponentiation b e)
+  (cond
+    ((=number? e 0) 1)
+    ((=number? e 1) b)
+    (else (list '** b e))))
+; Also extended deriv above.
+
+(display (deriv (make-exponentiation 'x 3) 'x))
+
+
+(display "\n\nex-2.57") (newline)
+
+(display "\n\nex-2.58") (newline)