From 187f699a8192305aed8c488046482f8f407dec3d Mon Sep 17 00:00:00 2001
From: Ivar Nesje <ivarne@gmail.com>
Date: Sat, 29 Jun 2013 08:20:13 +0200
Subject: [PATCH 1/3] Fixed error in "The Quotient Rule"

Differentiation of a fraction is wrong if the numerator or denominator independent of the variable differentiated with respect to.
It looks like somebody forgot to divide by (denominator)^2 for the special cases where one of the derivatives is 0
---
 src/differentiate.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/differentiate.jl b/src/differentiate.jl
index 11aa16a..af770e2 100644
--- a/src/differentiate.jl
+++ b/src/differentiate.jl
@@ -105,9 +105,9 @@ function differentiate(::SymbolParameter{:/}, args, wrt)
     if xp == 0 && yp == 0
         return 0
     elseif xp == 0
-        return :( -$yp * $x )
+        return :( -$yp * $x / $y^2 )
     elseif yp == 0
-        return :( $xp * $y )
+        return :( $xp / $y )
     else
         return :( ($xp * $y - $x * $yp) / $y^2 )
     end

From 0d2104275f545dc450a465fee44419692ce7d4b5 Mon Sep 17 00:00:00 2001
From: ivarne <ivarne@gmail.com>
Date: Sat, 29 Jun 2013 15:43:40 +0200
Subject: [PATCH 2/3] Added test of The Quotient Rule

---
 test/symbolic.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/test/symbolic.jl b/test/symbolic.jl
index 6e4b584..1332a08 100644
--- a/test/symbolic.jl
+++ b/test/symbolic.jl
@@ -7,6 +7,9 @@
 @assert isequal(differentiate(:(x + x), :x), 2)
 @assert isequal(differentiate(:(x - x), :x), 0)
 @assert isequal(differentiate(:(2 * x), :x), 2)
+@assert isequal(differentiate(:(2 / x), :x), :(-2 / x^2))
+@assert isequal(differentiate(:(x / 2), :x), 0.5)
+@assert isequal(differentiate(:(sin(x) / x), :x), :((cos(x) * x - sin(x)) / x^2))
 @assert isequal(differentiate(:(x * 2), :x), 2)
 @assert isequal(differentiate(:(a * x), :x), :a)
 @assert isequal(differentiate(:(x * a), :x), :a)

From 45c1d1be37d407f32bff0bd7b65b5291a57badd9 Mon Sep 17 00:00:00 2001
From: ivarne <ivarne@gmail.com>
Date: Mon, 1 Jul 2013 21:17:14 +0200
Subject: [PATCH 3/3] Removed unnecessary check in differentiate{:^}

---
 src/differentiate.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/differentiate.jl b/src/differentiate.jl
index af770e2..16aba4c 100644
--- a/src/differentiate.jl
+++ b/src/differentiate.jl
@@ -30,7 +30,7 @@ function differentiate(::SymbolParameter{:^}, args, wrt)
     yp = differentiate(y, wrt)
     if xp == 0 && yp == 0
         return 0
-    elseif xp != 0 && yp == 0
+    elseif yp == 0
         return :( $y * $xp * ($x ^ ($y - 1)) )
     else
         return :( $x ^ $y * ($xp * $y / $x + $yp * log($x)) )