diff --git a/xarray/core/datatree.py b/xarray/core/datatree.py
index 38f8f8cd495..65ff8667cb7 100644
--- a/xarray/core/datatree.py
+++ b/xarray/core/datatree.py
@@ -61,7 +61,7 @@
     import pandas as pd
 
     from xarray.core.datatree_io import T_DataTreeNetcdfEngine, T_DataTreeNetcdfTypes
-    from xarray.core.merge import CoercibleValue
+    from xarray.core.merge import CoercibleMapping, CoercibleValue
     from xarray.core.types import ErrorOptions, NetcdfWriteModes, ZarrWriteModes
 
 # """
@@ -954,23 +954,29 @@ def update(
 
         Just like `dict.update` this is an in-place operation.
         """
-        # TODO separate by type
         new_children: dict[str, DataTree] = {}
-        new_variables = {}
-        for k, v in other.items():
-            if isinstance(v, DataTree):
-                # avoid named node being stored under inconsistent key
-                new_child: DataTree = v.copy()
-                # Datatree's name is always a string until we fix that (#8836)
-                new_child.name = str(k)
-                new_children[str(k)] = new_child
-            elif isinstance(v, (DataArray, Variable)):
-                # TODO this should also accommodate other types that can be coerced into Variables
-                new_variables[k] = v
-            else:
-                raise TypeError(f"Type {type(v)} cannot be assigned to a DataTree")
-
-        vars_merge_result = dataset_update_method(self.to_dataset(), new_variables)
+        new_variables: CoercibleMapping
+
+        if isinstance(other, Dataset):
+            new_variables = other
+        else:
+            new_variables = {}
+            for k, v in other.items():
+                if isinstance(v, DataTree):
+                    # avoid named node being stored under inconsistent key
+                    new_child: DataTree = v.copy()
+                    # Datatree's name is always a string until we fix that (#8836)
+                    new_child.name = str(k)
+                    new_children[str(k)] = new_child
+                elif isinstance(v, (DataArray, Variable)):
+                    # TODO this should also accommodate other types that can be coerced into Variables
+                    new_variables[k] = v
+                else:
+                    raise TypeError(f"Type {type(v)} cannot be assigned to a DataTree")
+
+        vars_merge_result = dataset_update_method(
+            self.to_dataset(inherited=False), new_variables
+        )
         data = Dataset._construct_direct(**vars_merge_result._asdict())
 
         # TODO are there any subtleties with preserving order of children like this?
diff --git a/xarray/tests/test_datatree.py b/xarray/tests/test_datatree.py
index f2b58fa2489..f7cff17bab5 100644
--- a/xarray/tests/test_datatree.py
+++ b/xarray/tests/test_datatree.py
@@ -244,11 +244,6 @@ def test_update(self):
         dt: DataTree = DataTree()
         dt.update({"foo": xr.DataArray(0), "a": DataTree()})
         expected = DataTree.from_dict({"/": xr.Dataset({"foo": 0}), "a": None})
-        print(dt)
-        print(dt.children)
-        print(dt._children)
-        print(dt["a"])
-        print(expected)
         assert_equal(dt, expected)
 
     def test_update_new_named_dataarray(self):
@@ -268,14 +263,38 @@ def test_update_doesnt_alter_child_name(self):
     def test_update_overwrite(self):
         actual = DataTree.from_dict({"a": DataTree(xr.Dataset({"x": 1}))})
         actual.update({"a": DataTree(xr.Dataset({"x": 2}))})
-
         expected = DataTree.from_dict({"a": DataTree(xr.Dataset({"x": 2}))})
+        assert_equal(actual, expected)
 
-        print(actual)
-        print(expected)
-
+    def test_update_coordinates(self):
+        expected = DataTree.from_dict({"/": xr.Dataset(coords={"a": 1})})
+        actual = DataTree.from_dict({"/": xr.Dataset()})
+        actual.update(xr.Dataset(coords={"a": 1}))
         assert_equal(actual, expected)
 
+    def test_update_inherited_coords(self):
+        expected = DataTree.from_dict(
+            {
+                "/": xr.Dataset(coords={"a": 1}),
+                "/b": xr.Dataset(coords={"c": 1}),
+            }
+        )
+        actual = DataTree.from_dict(
+            {
+                "/": xr.Dataset(coords={"a": 1}),
+                "/b": xr.Dataset(),
+            }
+        )
+        actual["/b"].update(xr.Dataset(coords={"c": 1}))
+        assert_identical(actual, expected)
+
+        # DataTree.identical() currently does not require that non-inherited
+        # coordinates are defined identically, so we need to check this
+        # explicitly
+        actual_node = actual.children["b"].to_dataset(inherited=False)
+        expected_node = expected.children["b"].to_dataset(inherited=False)
+        assert_identical(actual_node, expected_node)
+
 
 class TestCopy:
     def test_copy(self, create_test_datatree):