Link to googleapis.dev documentation in READMEs. (#8705)
diff --git a/README.rst b/README.rst
index e44f55a..1740298 100644
--- a/README.rst
+++ b/README.rst
@@ -11,7 +11,7 @@
:target: https://pypi.org/project/google-api_core/
.. |versions| image:: https://img.shields.io/pypi/pyversions/google-api_core.svg
:target: https://pypi.org/project/google-api_core/
-.. _documentation: https://googleapis.github.io/google-cloud-python/latest/core/
+.. _documentation: https://googleapis.dev/python/google-api-core/latest
.. |compat_check_pypi| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=google-api-core
:target: https://python-compatibility-tools.appspot.com/one_badge_target?package=google-api-core
.. |compat_check_github| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Dapi_core