Partial Derivatives: Definitions and Examples

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

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Covers the calculation of partial derivatives of order 3 and the concept of differentiability in functions.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Covers the properties of functions in Rn and the computation of partial derivatives by induction.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Presents the solution to finding the second-order Taylor polynomial of a function.

Covers functions, including even and odd functions, periodicity, and function operations.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.