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{{Use dmy dates|date=December 2023}}
{{Calculus}}
In [[real analysis]], a branch of [[mathematics]], the '''inverse function theorem''' is a [[theorem]] that asserts that, if a [[real function]] ''f'' has a [[continuously differentiable function|continuous derivative]] near a point where its derivative is nonzero, then, near this point, ''f'' has an [[inverse function]]. The inverse function is also [[differentiable function|differentiable]], and the ''[[inverse function rule]]'' expresses its derivative as the [[multiplicative inverse]] of the derivative of ''f''.
The theorem applies verbatim to [[complex-valued function]]s of a [[complex number|complex variable]]. It generalizes to functions from
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