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differentiable_function [2016/01/23 19:05]
nikolaj
differentiable_function [2016/01/23 19:06]
nikolaj
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 ----- -----
-=== Reference === 
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Differentiable_function|Differentiable function]] 
- 
 === Theorems === === Theorems ===
 Let $f(0)=0$, then Let $f(0)=0$, then
  
-$f(y\ f^{-1}(x))\ y^{-1}=x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$+$\dfrac{ ​f(y\ f^{-1}(x)) ​}{y} =x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ 
 + 
 +=== Reference === 
 +Wikipedia: [[http://​en.wikipedia.org/​wiki/​Differentiable_function|Differentiable function]]
  
 ----- -----
 === Context === === Context ===
 [[Fréchet derivative]],​ [[Iterated function]] [[Fréchet derivative]],​ [[Iterated function]]
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