Replace derivative with educe

[weikengchen]

Description

This PR corresponds to #831 and replaces all derivative usage with educe, which is a more modern solution that has gained some popularity already.

closes: #831

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Before we can merge this PR, please make sure that all the following items have been
checked off. If any of the checklist items are not applicable, please leave them but
write a little note why.

• Targeted PR against correct branch (master)
• Linked to GitHub issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Added a relevant changelog entry to the Pending section in CHANGELOG.md
• Re-reviewed Files changed in the GitHub PR explorer

N/A:

• Wrote unit tests
• Updated relevant documentation in the code