During April 2025, Michael Howard enhanced the mphowardlab/essential-math repository by developing comprehensive documentation for partial derivatives, focusing on the inversion and chain rules. He applied his expertise in calculus and technical writing to create example-driven explanations that clarify complex mathematical concepts for users. The documentation, written in Markdown, included concrete mathematical examples and updated contributor credits to foster collaboration. This work improved user guidance and onboarding, reduced confusion for those implementing numerical methods, and aligned the project with best practices for technical math documentation. The depth of the enhancement supports maintainability and encourages correct downstream adoption of mathematical methods.