diff --git a/src/Data/Derivative.hs b/src/Data/Derivative.hs
--- a/src/Data/Derivative.hs
+++ b/src/Data/Derivative.hs
@@ -124,6 +124,10 @@
   negateV = fmap     negateV
   (^+^)   = liftA2   (^+^)
 
+instance (InnerSpace u s, InnerSpace s s') =>
+     InnerSpace (a :> u) (a :> s) where
+  (<.>) = distribD (<.>) (<.>)
+
 -- | Chain rule.
 (@.) :: (b :~> c) -> (a :~> b) -> (a :~> c)
 (h @. g) a0 = D c0 (c' @. b')
diff --git a/vector-space.cabal b/vector-space.cabal
--- a/vector-space.cabal
+++ b/vector-space.cabal
@@ -1,5 +1,5 @@
 Name:                vector-space
-Version:             0.1.2
+Version:             0.1.3
 Synopsis: 	     Vector & affine spaces, plus derivatives
 Category:            math
 Description: