Lectures related to Derivatives: Definition and Examples

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.

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

Covers the definition of differentiable functions and explores the representation of the remainder in derivatives.

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

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

Explains partial derivatives, Hessienne matrix, and their properties.

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

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Explores the limit of a sequence and its convergence properties, including boundedness and monotonicity.

Explores Taylor series expansions for derivatives and integrals, including practical applications.

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

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.

Explains definitions and remarks about closed intervals in functions.

Explores algebraic operations on limited developments and their consequences on differentiable functions, illustrated through examples.

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

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

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.