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In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...
For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point ; then is injective (or bijective onto the image) in a neighborhood of , the inverse is continuously differentiable near = (), and the derivative of the inverse function at is the reciprocal of the derivative of at : ′ = ′ = ′ (()).
For a continuous function on the real line, one branch is required between each pair of local extrema. For example, the inverse of a cubic function with a local maximum and a local minimum has three branches (see the adjacent picture). The arcsine is a partial inverse of the sine function.
Implicit function theorem; Increment theorem; Integral of inverse functions; Integration by parts; Integration using Euler's formula; Intermediate value theorem; Inverse function rule; Inverse function theorem
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
Lacoste is using AI tech Vrai to detect counterfeit returns. Return fraud costs retailers billions, with billions lost globally. Amazon and other retailers face scams exploiting return policies ...
The MLB world lost its all-time leader in stolen bases on Saturday with the death of Rickey Henderson, who was among baseball's brightest stars of the 1980s and '90s.. Henderson will always be ...
PARIS (Reuters) -Iran's acceleration in its enrichment of uranium to close to bomb grade is "extremely serious", has no civilian justification and contradicts Tehran's assertions on wanting ...