Smooth Piecewise Arcs Integration

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Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Explores finding the equation of the tangent line to a function's graph at a point.

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Explores the definition of connections for smooth vector fields on manifolds.

Explores finding tangent equations and slopes through derivatives.

Explains the Jacobian matrix and derivative of composite functions with examples.

Explains partial derivatives, Hessienne matrix, and their properties.

Explores derivability, continuity, and composite functions with illustrative examples.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.