diff --git a/src/awkward/_connect/jax/reducers.py b/src/awkward/_connect/jax/reducers.py
index 51492cabfd..469b9b4d67 100644
--- a/src/awkward/_connect/jax/reducers.py
+++ b/src/awkward/_connect/jax/reducers.py
@@ -111,7 +111,16 @@ def apply(
         shifts: ak.index.Index | None,
         outlength: ShapeItem,
     ) -> ak.contents.NumpyArray:
-        raise RuntimeError("Cannot differentiate through count_zero")
+        assert isinstance(array, ak.contents.NumpyArray)
+        result = jax.numpy.ones_like(array.data, dtype=array.dtype)
+        result = jax.ops.segment_sum(result, parents.data)
+
+        if np.issubdtype(array.dtype, np.complexfloating):
+            return ak.contents.NumpyArray(
+                result.view(array.dtype), backend=array.backend
+            )
+        else:
+            return ak.contents.NumpyArray(result, backend=array.backend)
 
 
 @overloads(_reducers.CountNonzero)
@@ -169,7 +178,7 @@ def apply(
             return ak.contents.NumpyArray(
                 array.backend.nplike.asarray(result, dtype=array.dtype)
             )
-        elif array.dtype.type in (np.complex128, np.complex64):
+        elif np.issubdtype(array.dtype, np.complexfloating):
             return ak.contents.NumpyArray(result.view(array.dtype))
         else:
             return ak.contents.NumpyArray(result, backend=array.backend)
@@ -200,7 +209,7 @@ def apply(
             jax.ops.segment_sum(jax.numpy.log(array.data), parents.data)
         )
 
-        if array.dtype.type in (np.complex128, np.complex64):
+        if np.issubdtype(array.dtype, np.complexfloating):
             return ak.contents.NumpyArray(
                 result.view(array.dtype), backend=array.backend
             )
@@ -318,7 +327,7 @@ def apply(
         result = jax.ops.segment_min(array.data, parents.data)
         result = jax.numpy.minimum(result, self._min_initial(self.initial, array.dtype))
 
-        if array.dtype.type in (np.complex128, np.complex64):
+        if np.issubdtype(array.dtype, np.complexfloating):
             return ak.contents.NumpyArray(
                 array.backend.nplike.asarray(
                     result.view(array.dtype), dtype=array.dtype
@@ -379,7 +388,7 @@ def apply(
         result = jax.ops.segment_max(array.data, parents.data)
 
         result = jax.numpy.maximum(result, self._max_initial(self.initial, array.dtype))
-        if array.dtype.type in (np.complex128, np.complex64):
+        if np.issubdtype(array.dtype, np.complexfloating):
             return ak.contents.NumpyArray(
                 array.backend.nplike.asarray(
                     result.view(array.dtype), dtype=array.dtype
diff --git a/tests/test_2638_mean_and_count_grads.py b/tests/test_2638_mean_and_count_grads.py
new file mode 100644
index 0000000000..12c7934e86
--- /dev/null
+++ b/tests/test_2638_mean_and_count_grads.py
@@ -0,0 +1,32 @@
+# BSD 3-Clause License; see https://github.com/scikit-hep/awkward/blob/main/LICENSE
+
+from __future__ import annotations
+
+import pytest
+
+import awkward as ak
+
+jax = pytest.importorskip("jax")
+
+
+def test():
+    ak.jax.register_and_check()
+
+    array = ak.Array([[1.0, 2.0, 3.0], [], [4.0, 5.0]], backend="jax")
+
+    val_mean, grad_mean = jax.value_and_grad(ak.mean, argnums=0)(array)
+    _, grad_sum = jax.value_and_grad(ak.sum, argnums=0)(array)
+    val_count, grad_count = jax.value_and_grad(ak.count, argnums=0)(array)
+
+    assert val_mean == 3
+    assert ak.all(
+        grad_mean == ak.Array([[0.2, 0.2, 0.2], [], [0.2, 0.2]], backend="jax")
+    )
+
+    # mean is treated as scaled sum
+    assert ak.all(grad_mean == grad_sum / val_count)
+
+    assert val_count == 5
+    assert ak.all(
+        grad_count == ak.Array([[0.0, 0.0, 0.0], [], [0.0, 0.0]], backend="jax")
+    )