Linked from

The 25 pages that link to Differentiability, each with the reason it gives.

• DerivativeRelated: It distinguishes points where the instantaneous rate is well-defined from points where it is not.

• Chain ruleRelated: The standard chain rule requires differentiability of the component functions at the relevant points.

• Real analysisRelated: Derivatives arise from limits of difference quotients.

• Tangent lineRelated: Differentiability guarantees a well-defined tangent direction for a graph at that point.

• Taylor's theoremRelated: The theorem requires enough derivatives for the stated polynomial degree and remainder.

• Karl WeierstrassRelated: The Weierstrass function shows that continuity alone does not guarantee differentiability anywhere.

• Implicit differentiationRelated: A smooth local curve is needed for its slope to be described by a derivative.

• L'Hôpital's ruleRelated: The numerator and denominator must be differentiable in the relevant punctured interval.

• Envelope theoremRelated: Differentiability conditions determine when the envelope formula yields an ordinary derivative.

• Hotelling's lemmaRelated: The standard derivative form of the lemma requires a differentiable profit function.

• Roy's identityRelated: The ratio requires the indirect utility function to have usable price and income derivatives.

• Differentiation rulesRelated: Rules require differentiable inputs wherever their formulas are applied.

• Interior extremum theoremRelated: Differentiability supplies the local rate of change whose value the theorem constrains.

• Symmetry of second derivativesRelated: Existence of second partial derivatives alone does not ensure their symmetry.