Lectures related to Differentiable Functions in R²

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

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

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

Covers differentiable functions, derivatives, and tangent planes in mathematics.

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

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

Covers the derivative of the reciprocal function and its properties.

Introduces the study of functions defined by power series and emphasizes the importance of separately considering boundary points.

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

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

Explains differentiability in LR functions and introduces the Jacobian matrix.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Explores differentiability, tangent lines, and graph interpretation.

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

Explores differentiability in two variables and the chain rule for compositions.

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

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

Covers the derivative of the composition of two functions and the chain rule theorem.

Covers continuity, differentiability, and applications in calculus with an emphasis on fundamental concepts.

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