Differentiable function
Set
| context | $X,Y$ … Banach spaces with topology |
| context | $n\in \mathbb N$ |
| definiendum | $f\in C^n(X,Y)$ |
| postulate | $\forall(k\le n).\,D^k f$ … continuous |
Theorems
Let
$f(0)=0\neq f'(0)$,
then
$\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''(0)}{f'(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$
Reference
Wikipedia: Differentiable function
Context
