diff --git a/src/differentiate.jl b/src/differentiate.jl
index 11aa16a..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)) ) 
@@ -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
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)