Differential Functions: Derivability and Gradient

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Covers the concept of functional derivatives and their calculation process with examples.

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

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

Explores the properties and methods of differentiable functions, including strong recurrence and demonstration techniques.

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

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

Explores higher-order partial derivatives and multi-variables in functions.

Covers differentiability theorems and methods to check for differentiability in functions.

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