diff --git a/CHANGELOG.md b/CHANGELOG.md
index 65a30703b41..862f9a3c4c4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,8 +12,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added Specificity metric ([#210](https://github.com/PyTorchLightning/metrics/pull/210))
 
 
-- Added `is_differentiable` property to `AUC`, `AUROC`, `CohenKappa` and `AveragePrecision` ([#178](https://github.com/PyTorchLightning/metrics/pull/178))
-
+- Added `is_differentiable` property:
+    * To `AUC`, `AUROC`, `CohenKappa` and `AveragePrecision` ([#178](https://github.com/PyTorchLightning/metrics/pull/178))
+    * To `PearsonCorrCoef`, `SpearmanCorrcoef`, `R2Score` and `ExplainedVariance` ([#225](https://github.com/PyTorchLightning/metrics/pull/225))
 
 - Added `add_metrics` method to `MetricCollection` for adding additional metrics after initialization ([#221](https://github.com/PyTorchLightning/metrics/pull/221))
 
@@ -21,6 +22,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Added pre-gather reduction in the case of `dist_reduce_fx="cat"` to reduce communication cost ([#217](https://github.com/PyTorchLightning/metrics/pull/217))
 
 
+
 ### Changed
 
 - `MetricCollection` should return metrics with prefix on `items()`, `keys()` ([#209](https://github.com/PyTorchLightning/metrics/pull/209))
diff --git a/tests/regression/test_explained_variance.py b/tests/regression/test_explained_variance.py
index dd1c37a4969..5e6fdc25fb3 100644
--- a/tests/regression/test_explained_variance.py
+++ b/tests/regression/test_explained_variance.py
@@ -85,6 +85,12 @@ def test_explained_variance_functional(self, multioutput, preds, target, sk_metr
             metric_args=dict(multioutput=multioutput),
         )
 
+    def test_explained_variance_differentiability(self, multioutput, preds, target, sk_metric):
+        self.run_differentiability_test(
+            preds=preds, target=target, metric_module=ExplainedVariance, metric_functional=explained_variance,
+            metric_args={'multioutput': multioutput}
+        )
+
     @pytest.mark.skipif(
         not _TORCH_GREATER_EQUAL_1_6, reason='half support of core operations on not support before pytorch v1.6'
     )
diff --git a/tests/regression/test_pearson.py b/tests/regression/test_pearson.py
index 91ecc56489e..6c17ab0293e 100644
--- a/tests/regression/test_pearson.py
+++ b/tests/regression/test_pearson.py
@@ -69,6 +69,11 @@ def test_pearson_corrcoef_functional(self, preds, target):
             preds=preds, target=target, metric_functional=pearson_corrcoef, sk_metric=_sk_pearsonr
         )
 
+    def test_pearson_corrcoef_differentiability(self, preds, target):
+        self.run_differentiability_test(
+            preds=preds, target=target, metric_module=PearsonCorrcoef, metric_functional=pearson_corrcoef
+        )
+
     # Pearson half + cpu does not work due to missing support in torch.sqrt
     @pytest.mark.xfail(reason="PearsonCorrcoef metric does not support cpu + half precision")
     def test_pearson_corrcoef_half_cpu(self, preds, target):
diff --git a/tests/regression/test_r2score.py b/tests/regression/test_r2score.py
index 699d6d67f11..b1ffd2cc0fb 100644
--- a/tests/regression/test_r2score.py
+++ b/tests/regression/test_r2score.py
@@ -93,6 +93,12 @@ def test_r2_functional(self, adjusted, multioutput, preds, target, sk_metric, nu
             metric_args=dict(adjusted=adjusted, multioutput=multioutput),
         )
 
+    def test_r2_differentiabilit(self, adjusted, multioutput, preds, target, sk_metric, num_outputs):
+        self.run_differentiability_test(
+            preds=preds, target=target, metric_module=partial(R2Score, num_outputs=num_outputs),
+            metric_functional=r2score, metric_args=dict(adjusted=adjusted, multioutput=multioutput)
+        )
+
     @pytest.mark.skipif(
         not _TORCH_GREATER_EQUAL_1_6, reason='half support of core operations on not support before pytorch v1.6'
     )
diff --git a/tests/regression/test_spearman.py b/tests/regression/test_spearman.py
index 45e64f65e8c..64cc1efed73 100644
--- a/tests/regression/test_spearman.py
+++ b/tests/regression/test_spearman.py
@@ -82,6 +82,11 @@ def test_spearman_corrcoef(self, preds, target, ddp, dist_sync_on_step):
     def test_spearman_corrcoef_functional(self, preds, target):
         self.run_functional_metric_test(preds, target, spearman_corrcoef, _sk_metric)
 
+    def test_spearman_corrcoef_differentiability(self, preds, target):
+        self.run_differentiability_test(
+            preds=preds, target=target, metric_module=SpearmanCorrcoef, metric_functional=spearman_corrcoef
+        )
+
     # Spearman half + cpu does not work due to missing support in torch.arange
     @pytest.mark.xfail(reason="Spearman metric does not support cpu + half precision")
     def test_spearman_corrcoef_half_cpu(self, preds, target):
diff --git a/torchmetrics/regression/explained_variance.py b/torchmetrics/regression/explained_variance.py
index a76980135dc..f5e3b2de186 100644
--- a/torchmetrics/regression/explained_variance.py
+++ b/torchmetrics/regression/explained_variance.py
@@ -131,3 +131,7 @@ def compute(self):
             self.sum_squared_target,
             self.multioutput,
         )
+
+    @property
+    def is_differentiable(self):
+        return True
diff --git a/torchmetrics/regression/pearson.py b/torchmetrics/regression/pearson.py
index f6e56065f49..21196c50a38 100644
--- a/torchmetrics/regression/pearson.py
+++ b/torchmetrics/regression/pearson.py
@@ -96,3 +96,7 @@ def compute(self):
         preds = dim_zero_cat(self.preds)
         target = dim_zero_cat(self.target)
         return _pearson_corrcoef_compute(preds, target)
+
+    @property
+    def is_differentiable(self):
+        return True
diff --git a/torchmetrics/regression/r2score.py b/torchmetrics/regression/r2score.py
index c5ee7a8b534..96b86a5e397 100644
--- a/torchmetrics/regression/r2score.py
+++ b/torchmetrics/regression/r2score.py
@@ -145,3 +145,7 @@ def compute(self) -> Tensor:
         return _r2score_compute(
             self.sum_squared_error, self.sum_error, self.residual, self.total, self.adjusted, self.multioutput
         )
+
+    @property
+    def is_differentiable(self):
+        return True
diff --git a/torchmetrics/regression/spearman.py b/torchmetrics/regression/spearman.py
index b7ac2c31288..3bb0d39ed28 100644
--- a/torchmetrics/regression/spearman.py
+++ b/torchmetrics/regression/spearman.py
@@ -94,3 +94,7 @@ def compute(self):
         preds = dim_zero_cat(self.preds)
         target = dim_zero_cat(self.target)
         return _spearman_corrcoef_compute(preds, target)
+
+    @property
+    def is_differentiable(self):
+        return False