Derivatives: Definition and Examples

Related lectures (55)

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

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

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

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

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

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

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Covers the derivative of the reciprocal function and its properties.

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

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

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

Explains partial derivatives, Hessienne matrix, and their properties.

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

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

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