--- a/NEWS
+++ b/NEWS
@@ -34,6 +34,7 @@
       __error_text__
       error_text
       is_duplicate_entry
+      polyderiv
       studentize
       sylvester_matrix
 

--- a/scripts/deprecated/module.mk
+++ b/scripts/deprecated/module.mk
@@ -18,6 +18,7 @@
   deprecated/isstr.m \
   deprecated/krylovb.m \
   deprecated/perror.m \
+  deprecated/polyderiv.m \
   deprecated/replot.m \
   deprecated/saveimage.m \
   deprecated/setstr.m \

rename from scripts/polynomial/polyderiv.m
rename to scripts/deprecated/polyderiv.m
--- a/scripts/polynomial/polyderiv.m
+++ b/scripts/deprecated/polyderiv.m
@@ -36,6 +36,13 @@
 
 function [q, d] = polyderiv (p, a)
 
+  persistent warned = false;
+  if (! warned)
+    warned = true;
+    warning ("Octave:deprecated-function",
+             "polyderiv is obsolete and will be removed from a future version of Octave; please use polyder instead");
+  endif
+
   if (nargin == 1 || nargin == 2)
     if (! isvector (p))
       error ("polyderiv: argument must be a vector");

--- a/scripts/polynomial/module.mk
+++ b/scripts/polynomial/module.mk
@@ -10,7 +10,6 @@
   polynomial/poly.m \
   polynomial/polyaffine.m \
   polynomial/polyder.m \
-  polynomial/polyderiv.m \
   polynomial/polyfit.m \
   polynomial/polygcd.m \
   polynomial/polyint.m \

--- a/scripts/polynomial/polyder.m
+++ b/scripts/polynomial/polyder.m
@@ -1,4 +1,4 @@
-## Copyright (C) 1995-2011 John W. Eaton
+## Copyright (C) 1994-2011 John W. Eaton
 ##
 ## This file is part of Octave.
 ##
@@ -17,27 +17,84 @@
 ## <http://www.gnu.org/licenses/>.
 
 ## -*- texinfo -*-
-## @deftypefn  {Function File} {} polyderiv (@var{p})
-## @deftypefnx {Function File} {[@var{k}] =} polyderiv (@var{a}, @var{b})
-## @deftypefnx {Function File} {[@var{q}, @var{d}] =} polyderiv (@var{b}, @var{a})
-## An alias for @code{polyderiv}.
-## @seealso{polyderiv}
+## @deftypefn  {Function File} {} polyder (@var{p})
+## @deftypefnx {Function File} {[@var{k}] =} polyder (@var{a}, @var{b})
+## @deftypefnx {Function File} {[@var{q}, @var{d}] =} polyder (@var{b}, @var{a})
+## Return the coefficients of the derivative of the polynomial whose
+## coefficients are given by the vector @var{p}.  If a pair of polynomials
+## is given, return the derivative of the product @math{@var{a}*@var{b}}.
+## If two inputs and two outputs are given, return the derivative of the
+## polynomial quotient @math{@var{b}/@var{a}}.  The quotient numerator is
+## in @var{q} and the denominator in @var{d}.
+## @seealso{poly, polyint, polyreduce, roots, conv, deconv, residue,
+## filter, polygcd, polyval, polyvalm}
 ## @end deftypefn
 
-## Author: John W. Eaton
+## Author: Tony Richardson <arichard@stark.cc.oh.us>
+## Created: June 1994
+## Adapted-By: jwe
 
 function [q, d] = polyder (p, a)
 
-  if (nargin == 1)
-    q = polyderiv (p);
-  elseif (nargin == 2)
-    if (nargout == 2)
-      [q, d] = polyderiv (p, a);
+  if (nargin == 1 || nargin == 2)
+    if (! isvector (p))
+      error ("polyder: argument must be a vector");
+    endif
+    if (nargin == 2)
+      if (! isvector (a))
+        error ("polyder: argument must be a vector");
+      endif
+      if (nargout == 1)
+        ## derivative of p*a returns a single polynomial
+        q = polyder (conv (p, a));
+      else
+        ## derivative of p/a returns numerator and denominator
+        d = conv (a, a);
+        if (numel (p) == 1)
+          q = -p * polyder (a);
+        elseif (numel (a) == 1)
+          q = a * polyder (p);
+        else
+          q = conv (polyder (p), a) - conv (p, polyder (a));
+          q = polyreduce (q);
+        endif
+
+        ## remove common factors from numerator and denominator
+        x = polygcd (q, d);
+        if (length(x) != 1)
+          q = deconv (q, x);
+          d = deconv (d, x);
+        endif
+
+        ## move all the gain into the numerator
+        q = q/d(1);
+        d = d/d(1);
+      endif
     else
-      q = polyderiv (p, a);
+      lp = numel (p);
+      if (lp == 1)
+        q = 0;
+        return;
+      elseif (lp == 0)
+        q = [];
+        return;
+      endif
+
+      ## Force P to be a row vector.
+      p = p(:).';
+
+      q = p(1:(lp-1)) .* [(lp-1):-1:1];
     endif
   else
     print_usage ();
   endif
 
 endfunction
+
+
+%!assert(all (all (polyder ([1, 2, 3]) == [2, 2])));
+%!assert(polyder (13) == 0);
+
+%!error polyder ([]);
+%!error polyder ([1, 2; 3, 4]);
+