# Differences

This shows you the differences between two versions of the page.

 differentiable_function [2016/01/23 19:06]nikolaj differentiable_function [2016/01/23 19:07] (current)nikolaj Both sides previous revision Previous revision 2016/01/23 19:07 nikolaj 2016/01/23 19:06 nikolaj 2016/01/23 19:06 nikolaj 2016/01/23 19:05 nikolaj 2016/01/23 19:05 nikolaj 2015/04/21 11:12 nikolaj 2015/04/21 11:12 nikolaj 2015/04/21 11:11 nikolaj 2015/04/21 11:11 nikolaj 2015/04/21 11:11 nikolaj 2015/03/27 20:11 nikolaj 2014/10/29 20:55 nikolaj 2014/03/21 11:11 external edit2013/09/13 21:33 nikolaj 2013/09/13 20:34 nikolaj 2013/09/13 20:33 nikolaj 2013/09/13 20:31 nikolaj 2013/09/13 20:30 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:27 nikolaj 2013/09/13 20:25 nikolaj 2013/09/13 20:24 nikolaj 2013/09/13 20:23 nikolaj created 2016/01/23 19:07 nikolaj 2016/01/23 19:06 nikolaj 2016/01/23 19:06 nikolaj 2016/01/23 19:05 nikolaj 2016/01/23 19:05 nikolaj 2015/04/21 11:12 nikolaj 2015/04/21 11:12 nikolaj 2015/04/21 11:11 nikolaj 2015/04/21 11:11 nikolaj 2015/04/21 11:11 nikolaj 2015/03/27 20:11 nikolaj 2014/10/29 20:55 nikolaj 2014/03/21 11:11 external edit2013/09/13 21:33 nikolaj 2013/09/13 20:34 nikolaj 2013/09/13 20:33 nikolaj 2013/09/13 20:31 nikolaj 2013/09/13 20:30 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:29 nikolaj 2013/09/13 20:27 nikolaj 2013/09/13 20:25 nikolaj 2013/09/13 20:24 nikolaj 2013/09/13 20:23 nikolaj created Line 8: Line 8: ----- ----- === Theorems === === Theorems === - Let $f(0)=0\neq f'​(0)$,​ then + Let + + $f(0)=0\neq f'​(0)$, ​ + + then $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$