Lectures related to Differentiable Functions: Definitions and Properties

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

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

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Explores functions of class C^p, Hessian matrices, and methods to verify differentiability at a point.

Explores partial derivatives, differentiability conditions, and verification methods, emphasizing the importance of continuity.

Explores differentiable functions, Taylor approximations, and directional derivatives in open sets.

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.