Linked from

The 17 pages that link to Implicit function theorem, each with the reason it gives.

• Partial derivativeRelated: Its conditions and conclusions are expressed through partial derivatives.

• DifferentiabilityRelated: Differentiability lets a constraint define a locally smooth relationship between variables.

• Comparative staticsRelated: It can show how an equilibrium variable changes locally when a parameter changes.

• Inverse function theoremRelated: It is a closely related local theorem, often derived from the inverse function theorem.

• Level setRelated: It explains when a level set can locally be written as a smooth graph.

• Total derivativeRelated: It lets implicit dependencies be differentiated to find their contribution to a total derivative.

• Fréchet derivativeRelated: Its Banach-space version uses an invertible partial Fréchet derivative.

• Implicit differentiationRelated: It explains when an equation locally determines one variable as a differentiable function of another.

• Cramer's ruleRelated: Its derivative formulas use determinant reasoning closely related to Cramer's rule.

• Differentiable functionRelated: Differentiability and a nonsingular derivative allow local solution branches.

• Envelope theoremCompared with: It can track how the optimizer moves, while the envelope formula avoids that derivative.

• Parametric equationRelated: It explains when an implicit relation can locally be rewritten in parametric form.

• Implicit functionRelated: It states when an implicit equation really defines a local function.

• Lagrange inversion theoremRelated: Its local existence result complements inversion's explicit coefficient calculations.

• Weierstrass preparation theoremCompared with: It solves locally for a variable; preparation instead packages dependence into a polynomial.

• Differentiation rulesRelated: Its derivative formula relies on differentiating the defining equation.

• Function of a real variableRelated: It shows when a relation involving real variables determines a local function.