diff --git a/cpp/Pose2.cpp b/cpp/Pose2.cpp
index 41dd21daf..fd1a84acd 100644
--- a/cpp/Pose2.cpp
+++ b/cpp/Pose2.cpp
@@ -56,6 +56,22 @@ namespace gtsam {
 		Matrix H; transform_to(pose, point, boost::none, H); return H;
   }
 
+  /* ************************************************************************* */
+  static const Rot2 R_PI_2(0., 1.);
+	static Matrix DR1 = Matrix_(1, 3, 0., 0., 1.);
+
+  Matrix Dcompose1(const Pose2& p1, const Pose2& p2) {
+		Matrix R2_inv = p2.r().transpose();
+		Point2 Rt2_ = R_PI_2 * inverse(p2.r()) * p2.t();
+		Matrix Rt2 = Matrix_(2, 1, Rt2_.x(), Rt2_.y());
+		Matrix Dt1 = collect(2, &R2_inv, &Rt2);
+		return gtsam::stack(2, &Dt1, &DR1);
+  }
+
+  Matrix Dcompose2(const Pose2& p1, const Pose2& p2) {
+  	return eye(3);
+  }
+
   /* ************************************************************************* */
   Pose2 between(const Pose2& p1, const Pose2& p2, boost::optional<Matrix&> H1,
 			boost::optional<Matrix&> H2) {
diff --git a/cpp/Pose2.h b/cpp/Pose2.h
index 3be38d09e..53898cef7 100644
--- a/cpp/Pose2.h
+++ b/cpp/Pose2.h
@@ -76,9 +76,11 @@ namespace gtsam {
     return Pose2(inverse(pose.r()),
         pose.r().unrotate(Point2(-pose.t().x(), -pose.t().y()))); }
 
-  /** compose this transformation onto another (pre-multiply this*p1) */
+  /** compose this transformation onto another (first p1 and then p2) */
   inline Pose2 compose(const Pose2& p0, const Pose2& p1) {
-    return Pose2(p0.r()*p1.r(), p0.t() + p0.r()*p1.t()); }
+      return Pose2(p0.r()*p1.r(), p0.t() + p0.r()*p1.t()); }
+  Matrix Dcompose1(const Pose2& p1, const Pose2& p2);
+  Matrix Dcompose2(const Pose2& p1, const Pose2& p2);
 
   /** exponential and log maps around identity */
 
diff --git a/cpp/testPose2.cpp b/cpp/testPose2.cpp
index 35add58f8..dfa81d47a 100644
--- a/cpp/testPose2.cpp
+++ b/cpp/testPose2.cpp
@@ -120,10 +120,26 @@ TEST(Pose2, compose_a)
   Pose2 pose1(M_PI/4.0, Point2(sqrt(0.5), sqrt(0.5)));
   Pose2 pose2(M_PI/2.0, Point2(0.0, 2.0));
 
+  Pose2 actual = compose(pose1, pose2);
+  Matrix actualH1 = Dcompose1(pose1, pose2);
+  Matrix actualH2 = Dcompose2(pose1, pose2);
+
   Pose2 expected(3.0*M_PI/4.0, Point2(-sqrt(0.5), 3.0*sqrt(0.5)));
-  Pose2 actual = pose1 * pose2;
   CHECK(assert_equal(expected, actual));
 
+  Matrix expectedH1 = Matrix_(3,3,
+  		0.0, 1.0, 0.0,
+  	 -1.0, 0.0, 2.0,
+  		0.0, 0.0, 1.0
+  );
+  Matrix expectedH2 = eye(3);
+  Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  CHECK(assert_equal(expectedH1,actualH1));
+  CHECK(assert_equal(numericalH1,actualH1));
+  CHECK(assert_equal(expectedH2,actualH2));
+  CHECK(assert_equal(numericalH2,actualH2));
+
   Point2 point(sqrt(0.5), 3.0*sqrt(0.5));
   Point2 expected_point(-1.0, -1.0);
   Point2 actual_point1 = transform_to(pose1 * pose2, point);
@@ -143,6 +159,13 @@ TEST(Pose2, compose_b)
 
   Pose2 pose_actual_op = pose1 * pose2;
   Pose2 pose_actual_fcn = compose(pose1, pose2);
+  Matrix actualH1 = Dcompose1(pose1, pose2);
+  Matrix actualH2 = Dcompose2(pose1, pose2);
+
+  Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  CHECK(assert_equal(numericalH1,actualH1));
+  CHECK(assert_equal(numericalH2,actualH2));
 
   CHECK(assert_equal(pose_expected, pose_actual_op));
   CHECK(assert_equal(pose_expected, pose_actual_fcn));
@@ -159,6 +182,13 @@ TEST(Pose2, compose_c)
 
   Pose2 pose_actual_op = pose1 * pose2;
   Pose2 pose_actual_fcn = compose(pose1,pose2);
+  Matrix actualH1 = Dcompose1(pose1, pose2);
+  Matrix actualH2 = Dcompose2(pose1, pose2);
+
+  Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(compose, pose1, pose2, 1e-5);
+  CHECK(assert_equal(numericalH1,actualH1));
+  CHECK(assert_equal(numericalH2,actualH2));
 
   CHECK(assert_equal(pose_expected, pose_actual_op));
   CHECK(assert_equal(pose_expected, pose_actual_fcn));