Lectures related to Derivative: Derivation Rules

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Derivability and Chain Rule

Covers the demonstration of the chain rule and the theorem of Rolle.

Derivatives: Definition and Properties

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

Derivatives and Continuity

Covers continuous differentiability, the Bernoulli-l'Hôpital rule, and finding extrema using derivatives.

Derivability and Continuity

Explores derivability, continuity, and composite functions with illustrative examples.

Differentiability and Derivatives

Covers differentiability, derivatives, composite functions, linear approximation, and partial derivatives.

Inverse Function Identity

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Fourier Transform: Properties and Applications

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Derivative and Function Variation

Discusses conditions for functions to be strictly increasing or decreasing based on the derivative.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Power Functions: Properties and Derivatives

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Linear Approximation and Derivative Parametric

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

Partial Derivatives: Derivative of an Integral with Parameter-dependent Bounds

Covers the derivative of an integral with parameter-dependent bounds and the gradient.

Calculus of Variations: Some Topics

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Computing Derivatives: Derivatives and Algebraic Operations

Covers the computation of derivatives and the properties of differentiable functions.