diff --git a/jax/_src/api_util.py b/jax/_src/api_util.py
index 1bfce85d592c..eb5e7e8bf8de 100644
--- a/jax/_src/api_util.py
+++ b/jax/_src/api_util.py
@@ -283,15 +283,15 @@ def argnums_partial_except(f: lu.WrappedFun, static_argnums: tuple[int, ...],
   return _argnums_partial(f, dyn_argnums, tuple(fixed_args)), dyn_args
 
 @lu.transformation2
-def _argnums_partial(f, dyn_argnums, fixed_args, *dyn_args, **kwargs):
+def _argnums_partial(_fun, _dyn_argnums, _fixed_args, *dyn_args, **kwargs):
   sentinel = object()
-  args = [sentinel] * (len(fixed_args) + len(dyn_args))
-  for i, arg in zip(dyn_argnums, dyn_args):
+  args = [sentinel] * (len(_fixed_args) + len(dyn_args))
+  for i, arg in zip(_dyn_argnums, dyn_args):
     args[i] = arg
-  fixed_args_ = iter(fixed_args)
+  fixed_args_ = iter(_fixed_args)
   args = [next(fixed_args_).val if x is sentinel else x for x in args]
   assert next(fixed_args_, sentinel) is sentinel
-  return f(*args, **kwargs)
+  return _fun(*args, **kwargs)
 
 def argnames_partial_except(f: lu.WrappedFun, static_argnames: tuple[str, ...],
                             kwargs: dict[str, Any]):
@@ -315,9 +315,9 @@ def argnames_partial_except(f: lu.WrappedFun, static_argnames: tuple[str, ...],
   return _argnames_partial(f, WrapKwArgs(fixed_kwargs)), dyn_kwargs
 
 @lu.transformation2
-def _argnames_partial(f, fixed_kwargs: WrapKwArgs, *args, **dyn_kwargs):
-  kwargs = dict({k: v.val for k, v in fixed_kwargs.val.items()}, **dyn_kwargs)
-  return f(*args, **kwargs)
+def _argnames_partial(_fun, _fixed_kwargs: WrapKwArgs, *args, **dyn_kwargs):
+  kwargs = dict({k: v.val for k, v in _fixed_kwargs.val.items()}, **dyn_kwargs)
+  return _fun(*args, **kwargs)
 
 
 @lru_cache(maxsize=4096)
@@ -438,9 +438,9 @@ def flat_out_axes(
   return f, HashableFunction(out_axes, closure=(tuple(leaves), treedef))
 
 @lu.transformation_with_aux2
-def _flat_out_axes(f, store, leaves, treedef, *args, **kwargs):
-  ans = f(*args, **kwargs)
-  spec = tree_unflatten(treedef, leaves)
+def _flat_out_axes(_fun, _store, _leaves, _treedef, *args, **kwargs):
+  ans = _fun(*args, **kwargs)
+  spec = tree_unflatten(_treedef, _leaves)
   try:
     spec_flat = tuple(broadcast_prefix(spec, ans, is_leaf=lambda x: x is None))
   except ValueError:
@@ -451,7 +451,7 @@ def _flat_out_axes(f, store, leaves, treedef, *args, **kwargs):
             "that the `out_axes` argument to `pmap` is a pytree prefix of the "
             "pmapped function's output.")
     raise ValueError(msg) from None
-  store.store(spec_flat)
+  _store.store(spec_flat)
   return ans
 
 def check_callable(fun):
@@ -687,10 +687,10 @@ def _arg_names(fn_signature, args, kwargs, static_argnums, static_argnames,
                for path, l in generate_key_paths(x) if l is not static)
 
 @lu.transformation_with_aux2
-def result_paths(f, store, *args, **kwargs):
+def result_paths(_fun, _store, *args, **kwargs):
   "linear_util transform to get output pytree paths of pre-flattened function."
-  ans = f(*args, **kwargs)
-  store.store([keystr(path) for path, _ in generate_key_paths(ans)])
+  ans = _fun(*args, **kwargs)
+  _store.store([keystr(path) for path, _ in generate_key_paths(ans)])
   return ans
 
 def jaxpr_debug_info(jaxpr: core.Jaxpr, trace_debug: TracingDebugInfo | None,