diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 7111d54d65815..669265dddd4ff 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -558,7 +558,7 @@ Other
 - Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` incorrectly raising ``AssertionError`` instead of ``ValueError`` when invalid parameter combinations are passed (:issue:`36045`)
 - Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` with numeric values and string ``to_replace`` (:issue:`34789`)
 - Fixed bug in metadata propagation incorrectly copying DataFrame columns as metadata when the column name overlaps with the metadata name (:issue:`37037`)
-- Fixed metadata propagation in the :class:`Series.dt` and :class:`Series.str` accessors and :class:`DataFrame.duplicated` and :class:`DataFrame.stack` and :class:`DataFrame.unstack` and :class:`DataFrame.pivot` methods (:issue:`28283`)
+- Fixed metadata propagation in the :class:`Series.dt`, :class:`Series.str` accessors, :class:`DataFrame.duplicated`, :class:`DataFrame.stack`, :class:`DataFrame.unstack`, :class:`DataFrame.pivot`, :class:`DataFrame.append`, :class:`DataFrame.diff`, :class:`DataFrame.applymap` and :class:`DataFrame.update` methods (:issue:`28283`) (:issue:`37381`)
 - Bug in :meth:`Index.union` behaving differently depending on whether operand is a :class:`Index` or other list-like (:issue:`36384`)
 - Passing an array with 2 or more dimensions to the :class:`Series` constructor now raises the more specific ``ValueError``, from a bare ``Exception`` previously (:issue:`35744`)
 - Bug in ``accessor.DirNamesMixin``, where ``dir(obj)`` wouldn't show attributes defined on the instance (:issue:`37173`).
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 24b89085ac121..09a014af60861 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -7401,7 +7401,7 @@ def diff(self, periods: int = 1, axis: Axis = 0) -> DataFrame:
             return self - self.shift(periods, axis=axis)
 
         new_data = self._mgr.diff(n=periods, axis=bm_axis)
-        return self._constructor(new_data)
+        return self._constructor(new_data).__finalize__(self, "diff")
 
     # ----------------------------------------------------------------------
     # Function application
@@ -7780,7 +7780,7 @@ def infer(x):
                 return lib.map_infer(x, func, ignore_na=ignore_na)
             return lib.map_infer(x.astype(object)._values, func, ignore_na=ignore_na)
 
-        return self.apply(infer)
+        return self.apply(infer).__finalize__(self, "applymap")
 
     # ----------------------------------------------------------------------
     # Merging / joining methods
@@ -7917,12 +7917,14 @@ def append(
             to_concat = [self, *other]
         else:
             to_concat = [self, other]
-        return concat(
-            to_concat,
-            ignore_index=ignore_index,
-            verify_integrity=verify_integrity,
-            sort=sort,
-        )
+        return (
+            concat(
+                to_concat,
+                ignore_index=ignore_index,
+                verify_integrity=verify_integrity,
+                sort=sort,
+            )
+        ).__finalize__(self, method="append")
 
     def join(
         self, other, on=None, how="left", lsuffix="", rsuffix="", sort=False
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 1219fefd7ea92..978597e3c7686 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -689,7 +689,7 @@ def get_result(self):
 
         self._maybe_restore_index_levels(result)
 
-        return result
+        return result.__finalize__(self, method="merge")
 
     def _indicator_pre_merge(
         self, left: "DataFrame", right: "DataFrame"
@@ -1505,7 +1505,7 @@ def get_result(self):
         )
 
         typ = self.left._constructor
-        result = typ(result_data).__finalize__(self, method=self._merge_type)
+        result = typ(result_data)
 
         self._maybe_add_join_keys(result, left_indexer, right_indexer)
 
diff --git a/pandas/tests/generic/test_finalize.py b/pandas/tests/generic/test_finalize.py
index d7aadda990f53..46548a32cfeb7 100644
--- a/pandas/tests/generic/test_finalize.py
+++ b/pandas/tests/generic/test_finalize.py
@@ -178,20 +178,14 @@
         marks=not_implemented_mark,
     ),
     pytest.param(
-        (pd.DataFrame, frame_data, operator.methodcaller("diff")),
-        marks=not_implemented_mark,
-    ),
-    pytest.param(
-        (pd.DataFrame, frame_data, operator.methodcaller("applymap", lambda x: x)),
-        marks=not_implemented_mark,
+        (pd.DataFrame, frame_data, operator.methodcaller("applymap", lambda x: x))
     ),
     pytest.param(
         (
             pd.DataFrame,
             frame_data,
             operator.methodcaller("append", pd.DataFrame({"A": [1]})),
-        ),
-        marks=not_implemented_mark,
+        )
     ),
     pytest.param(
         (
@@ -199,7 +193,6 @@
             frame_data,
             operator.methodcaller("append", pd.DataFrame({"B": [1]})),
         ),
-        marks=not_implemented_mark,
     ),
     pytest.param(
         (