The Increment Theorem: Understanding Derivatives

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Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

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Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Explores the extension of the chain rule to higher dimensions and compositions of functions.