diff --git a/compile.sh b/compile.sh
new file mode 100644
index 0000000..f174fbe
--- /dev/null
+++ b/compile.sh
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+ar rcs lizfcm.a src/*
diff --git a/lizfcm.a b/lizfcm.a
new file mode 100644
index 0000000..1d27463
Binary files /dev/null and b/lizfcm.a differ
diff --git a/lizfcm.asd b/lizfcm.asd
deleted file mode 100644
index 3e8c289..0000000
--- a/lizfcm.asd
+++ /dev/null
@@ -1,39 +0,0 @@
-(asdf:defsystem "lizfcm"
-                :version "0.1.0"
-                :author "Elizabeth Hunt"
-                :license "MIT"
-                :components ((:module "src"
-                                      :components
-                                      ((:module "utils"
-                                                :components
-                                                ((:file "within-range" :depends-on ("package"))
-                                                 (:file "table" :depends-on ("package"))
-                                                 (:file "package")))
-                                       (:module "approx"
-                                                :components
-                                                ((:file "maceps" :depends-on ("package"))
-                                                 (:file "derivative" :depends-on ("package"))
-                                                 (:file "package")))
-                                       (:module "vector"
-                                                :components
-                                                ((:file "distance" :depends-on ("norm" "package"))
-                                                 (:file "norm" :depends-on ("package"))
-                                                 (:file "package")))))))
-
-
-(asdf:defsystem "lizfcm/tests"
-                :author "Elizabeth Hunt"
-                :license "MIT"
-                :depends-on (:fiveam
-                              :lizfcm)
-                :components ((:module "tests"
-                                      :components
-                                      ((:file "table" :depends-on ("suite"))
-                                       (:file "maceps" :depends-on ("suite"))
-                                       (:file "approx" :depends-on ("suite"))
-                                       (:file "vector" :depends-on ("suite"))
-                                       (:file "suite"))))
-                :perform (asdf:test-op (o c) (uiop:symbol-call
-                                               :fiveam :run!
-                                               (uiop:find-symbol* :lizfcm-test-suite :lizfcm/tests))))
-
diff --git a/src/approx/derivative.lisp b/src/approx,derivative.lisp
similarity index 59%
rename from src/approx/derivative.lisp
rename to src/approx,derivative.lisp
index 8aa171a..631a5c0 100644
--- a/src/approx/derivative.lisp
+++ b/src/approx,derivative.lisp
@@ -8,10 +8,18 @@
     (/ (- y2 y1)
        (- x2 x1))))
 
-(defun fwd-derivative-at (f x &optional (delta 0.01))
+(defun forward-derivative-at (f x &optional (delta 0.01))
   (let* ((x2 (+ x delta))
          (x1 x)
          (y2 (apply f (list x2)))
          (y1 (apply f (list x1))))
     (/ (- y2 y1)
        (- x2 x1))))
+
+(defun backward-derivative-at (f x &optional (delta 0.01))
+  (let* ((x2 x)
+         (x1 (- x delta))
+         (y2 (apply f (list x2)))
+         (y1 (apply f (list x1))))
+    (/ (- y2 y1)
+       (- x2 x1))))
diff --git a/src/approx/maceps.lisp b/src/approx,maceps.lisp
similarity index 100%
rename from src/approx/maceps.lisp
rename to src/approx,maceps.lisp
diff --git a/src/approx/package.lisp b/src/approx,package.lisp
similarity index 64%
rename from src/approx/package.lisp
rename to src/approx,package.lisp
index 67c6a90..a0eac80 100644
--- a/src/approx/package.lisp
+++ b/src/approx,package.lisp
@@ -2,5 +2,6 @@
 (defpackage lizfcm.approx
   (:use :cl)
   (:export :central-derivative-at
-           :fwd-derivative-at
+           :forward-derivative-at
+           :backward-derivative-at
            :compute-maceps))
diff --git a/src/lizfcm.asd b/src/lizfcm.asd
new file mode 100644
index 0000000..ee8beb0
--- /dev/null
+++ b/src/lizfcm.asd
@@ -0,0 +1,32 @@
+(asdf:defsystem "lizfcm"
+                :version "0.1.0"
+                :author "Elizabeth Hunt"
+                :license "MIT"
+                :components
+                ((:file "utils,within-range" :depends-on ("utils,package"))
+                 (:file "utils,table" :depends-on ("utils,package"))
+                 (:file "utils,package")
+                 (:file "approx,maceps" :depends-on ("approx,package"))
+                 (:file "approx,derivative" :depends-on ("approx,package"))
+                 (:file "approx,package")
+                 (:file "vector,distance" :depends-on ("vector,norm" "vector,package"))
+                 (:file "vector,norm" :depends-on ("vector,package"))
+                 (:file "vector,package")))
+
+
+(asdf:defsystem "lizfcm/tests"
+                :author "Elizabeth Hunt"
+                :license "MIT"
+                :depends-on
+                (:fiveam
+                  :lizfcm)
+                :components
+                ((:file "tests,table" :depends-on ("tests,suite"))
+                 (:file "tests,maceps" :depends-on ("tests,suite"))
+                 (:file "tests,approx" :depends-on ("tests,suite"))
+                 (:file "tests,vector" :depends-on ("tests,suite"))
+                 (:file "tests,suite"))
+                :perform
+                (asdf:test-op (o c) (uiop:symbol-call
+                                      :fiveam :run!
+                                      (uiop:find-symbol* :lizfcm-test-suite :lizfcm/tests))))
diff --git a/src/package.lisp b/src/package.lisp
deleted file mode 100644
index 88b10eb..0000000
--- a/src/package.lisp
+++ /dev/null
@@ -1,7 +0,0 @@
-(in-package :cl-user)
-(defpackage lizfcm.vector
-  (:use :cl)
-  (:export
-    :n-norm
-    :max-norm
-    :distance))
diff --git a/tests/approx.lisp b/src/tests,approx.lisp
similarity index 73%
rename from tests/approx.lisp
rename to src/tests,approx.lisp
index 588b16d..678ff8c 100644
--- a/tests/approx.lisp
+++ b/src/tests,approx.lisp
@@ -34,3 +34,15 @@
               (forward-derivative-at f x delta)
               f-prime-at-x
               accepted-delta))))
+
+(test bwd-derivative-at
+      :description "backward derivative at is within bounds"
+      (let ((f (lambda (x) (* x x)))
+            (x 2)
+            (accepted-delta 0.02)
+            (f-prime-at-x 4)
+            (delta 0.01))
+        (is (within-range-p
+              (backward-derivative-at f x delta)
+              f-prime-at-x
+              accepted-delta))))
diff --git a/tests/maceps.lisp b/src/tests,maceps.lisp
similarity index 100%
rename from tests/maceps.lisp
rename to src/tests,maceps.lisp
diff --git a/tests/suite.lisp b/src/tests,suite.lisp
similarity index 100%
rename from tests/suite.lisp
rename to src/tests,suite.lisp
diff --git a/tests/table.lisp b/src/tests,table.lisp
similarity index 100%
rename from tests/table.lisp
rename to src/tests,table.lisp
diff --git a/tests/vector.lisp b/src/tests,vector.lisp
similarity index 100%
rename from tests/vector.lisp
rename to src/tests,vector.lisp
diff --git a/src/utils/package.lisp b/src/utils,package.lisp
similarity index 100%
rename from src/utils/package.lisp
rename to src/utils,package.lisp
diff --git a/src/utils/table.lisp b/src/utils,table.lisp
similarity index 100%
rename from src/utils/table.lisp
rename to src/utils,table.lisp
diff --git a/src/utils/within-range.lisp b/src/utils,within-range.lisp
similarity index 100%
rename from src/utils/within-range.lisp
rename to src/utils,within-range.lisp
diff --git a/src/vector/distance.lisp b/src/vector,distance.lisp
similarity index 100%
rename from src/vector/distance.lisp
rename to src/vector,distance.lisp
diff --git a/src/vector/norm.lisp b/src/vector,norm.lisp
similarity index 100%
rename from src/vector/norm.lisp
rename to src/vector,norm.lisp
diff --git a/src/vector/package.lisp b/src/vector,package.lisp
similarity index 100%
rename from src/vector/package.lisp
rename to src/vector,package.lisp