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- Inverse_functions_and_differentiation abstract "In mathematics, the inverse of a function is a function that, in some fashion, "undoes" the effect of (see inverse function for a formal and detailed definition). The inverse of is denoted . The statements y = f(x) and x = f −1(y) are equivalent.Their two derivatives, assuming they exist, are reciprocal, as the Leibniz notation suggests; that is:This is a direct consequence of the chain rule, sinceand the derivative of with respect to is 1.Writing explicitly the dependence of on and the point at which the differentiation takes place and using Lagrange's notation, the formula for the derivative of the inverse becomesGeometrically, a function and inverse function have graphs that are reflections, in the line y = x. This reflection operation turns the gradient of any line into its reciprocal.Assuming that has an inverse in a neighbourhood of and that its derivative at that point is non-zero, its inverse is guaranteed to be differentiable at and have a derivative given by the above formula.".
- Inverse_functions_and_differentiation thumbnail Umkehrregel_2.png?width=300.
- Inverse_functions_and_differentiation wikiPageID "148064".
- Inverse_functions_and_differentiation wikiPageRevisionID "599181355".
- Inverse_functions_and_differentiation hasPhotoCollection Inverse_functions_and_differentiation.
- Inverse_functions_and_differentiation subject Category:Differentiation_rules.
- Inverse_functions_and_differentiation subject Category:Inverse_functions.
- Inverse_functions_and_differentiation comment "In mathematics, the inverse of a function is a function that, in some fashion, "undoes" the effect of (see inverse function for a formal and detailed definition). The inverse of is denoted .".
- Inverse_functions_and_differentiation label "Derivada de la función inversa".
- Inverse_functions_and_differentiation label "Inverse functions and differentiation".
- Inverse_functions_and_differentiation label "Regola della funzione inversa".
- Inverse_functions_and_differentiation label "Umkehrregel".
- Inverse_functions_and_differentiation label "Производная обратной функции".
- Inverse_functions_and_differentiation label "دالات عكسية و تفاضلها".
- Inverse_functions_and_differentiation sameAs Umkehrregel.
- Inverse_functions_and_differentiation sameAs Derivada_de_la_función_inversa.
- Inverse_functions_and_differentiation sameAs Regola_della_funzione_inversa.
- Inverse_functions_and_differentiation sameAs m.012zvg.
- Inverse_functions_and_differentiation sameAs Q2143416.
- Inverse_functions_and_differentiation sameAs Q2143416.
- Inverse_functions_and_differentiation wasDerivedFrom Inverse_functions_and_differentiation?oldid=599181355.
- Inverse_functions_and_differentiation depiction Umkehrregel_2.png.
- Inverse_functions_and_differentiation isPrimaryTopicOf Inverse_functions_and_differentiation.
