Lectures related to Derivative and Function Variation

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

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

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

Explores derivatives, local extrema, and function variation in mathematical analysis.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

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

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

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores the conditions for a function to be continuous and differentiable.

Covers the rules of derivation and how to calculate derivatives.

Covers the concepts of increasing and decreasing functions and the relationship between the derivative and monotonicity.

Explores Rolle's Theorem and its corollaries, including applications and proofs.

Explores the immediate consequences of f' = 0 and monotonicity on intervals.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores the theorems of continuity and derivative numbers, including strict monotonicity and the Newton ratio.