Derivability Study: Behavioral Rules and Examples

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

Explores Bernoulli and K properties in smooth dynamics, including equivalence, examples, and implications.

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

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.

Explores Rolle's theorem application and function extrema conditions.

Covers the properties and operations of convex functions.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.