Partial Derivatives: Examples

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Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Partial Derivatives: Introduction

Introduces partial derivatives in functions of several variables and their properties.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Partial Derivatives: Functions and Definitions

Explores partial derivatives of functions with multiple variables, emphasizing their definitions and properties.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Gradient and Taylor Formula

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

Partial Derivatives: Definitions and Interpretations

Explores partial derivatives, their interpretations, and geometric applications in multivariable functions.

Partial Derivatives: Understanding and Applications

Explores the computation and significance of partial derivatives in determining rates of change.

Directional Derivatives and Tangent Planes

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

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.