Differentiability and Tangent Planes

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Related lectures (23)

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Functions and Coordinate Changes

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

Chain Rules

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

Differentiability and Derivatives

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

Derivatives and Approximations: Logarithmic Functions

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

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Linear Approximation and Derivative Parametric

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

Differentiability of Functions in Two Variables

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

Partial Derivatives and Matrix Hessians

Covers partial derivatives, Hessian matrices, and their importance for functions with multiple variables.

Partial Derivatives: Understanding and Applications

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

Differentiability and Tangent Planes in Multivariable Functions

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