Add automatic differentiation algorithm (#10977)

* Added automatic differentiation algorithm

* file name changed

* Resolved pre commit errors

* updated dependency

* added noqa for ignoring check

* adding typing_extension for adding Self type in __new__

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* sorted requirement.text dependency

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* resolved ruff

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>