Theorems in analysis | Algebraic geometry | Differential calculus | Differential topology | Multivariable calculus

Implicit function

In mathematics, an implicit equation is a relation of the form where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation of the unit circle defines y as an implicit function of x if −1 ≤ x ≤ 1, and y is restricted to nonnegative values. The implicit function theorem provides conditions under which some kinds of implicit equations define implicit functions, namely those that are obtained by equating to zero multivariable functions that are continuously differentiable. (Wikipedia).

Implicit function
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From playlist Find the Derivative using Implicit Differentiation

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Inverse function | Functional equation | Differential of a function | Chain rule | Differentiable function | Mathematical analysis | Marginal rate of substitution | Parameter | Polynomial | Quartic equation | Contour line | Level set | Partial derivative | Implicit function theorem | Relation (mathematics) | Isosurface | Neighbourhood (mathematics) | Logarithmic differentiation | Marginal rate of technical substitution | Value (mathematics) | Mathematics | Unit circle | Function (mathematics) | Closed-form expression | Argument of a function | Real number | Algebraic geometry | Algebraic expression | Calculus | Indifference curve | Cubic equation | Singular point of a curve | Related rates | Total derivative | Tangent | Implicit curve