# Difference between revisions of "Inverse function theorem"

From Calculus

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## Revision as of 22:39, 21 September 2011

This article is about adifferentiation rule, i.e., a rule for differentiating a function expressed in terms of other functions whose derivatives are known.

View other differentiation rules

## Contents

## Statement

### Simple version at a specific point

Suppose is a function of one variable that is a one-one function and is in the domain of . Suppose is [differentiable function|differentiable]] at and . Suppose further that the derivative is nonzero, i.e., . Then:

The inverse function is differentiable at , and further:

### Simple version at a generic point

Suppose is a function of one variable that is a one-one function. Then, the formula for the derivative of the inverse function is as follows:

with the formula applicable at all points in the range of for which exists and is nonzero.

### One-sided versions

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### Infinity-sensitive versions

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