Under a suitable non-degeneracy condition on its partial derivatives, an equation relating several variables can be locally solved for one variable as a differentiable function of the others. It is a basic tool of multivariable calculus and differential geometry.
Facts
StatementThe implicit function theorem gives sufficient conditions under which an equation relating several variables can be solved for one of those variables as a function of the others near a given point. 1 Classification
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Sources
1. Implicit Function Theorem (Wikipedia)
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In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F(x,y)=0 can also be specified as the graph of a function f
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