Lectures related to Derivatives of Composite Functions

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Differential Calculus: Definition and Derivability

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

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.

Chain Rules

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

Derivability and Composition of Functions

Explores derivability and function composition with examples.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Linear Applications and Matrix Derivatives

Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.

Derivability and Chain Rule

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

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Derivatives and Continuity

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

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Derivatives and Tangents

Introduces derivatives, tangent lines, rules of differentiation, and practical examples.

Power Functions: Properties and Derivatives

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

Derivatives and Hyperbolic Functions

Covers derivatives, hyperbolic functions, and theorems of Rolle and finite increments.

The Increment Theorem: Understanding Derivatives

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Tangent to Graph of a Function

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

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Calculus Fundamentals

Covers the fundamentals of calculus, including limits, derivatives, and integrals.

Demonstration of Theorem

Covers the demonstration of a theorem using mathematical expressions and hypotheses.