===== Fréchet derivative =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X,Y$ ... Banach spaces with topology |
| @#55CCEE: context     | @#55CCEE: $\mathcal O$ ... open in $X$ |
| @#FFBB00: definiendum | @#FFBB00: $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ |
| @#FFBB00: definiendum | @#FFBB00: $Df:=x\mapsto J_x^f$ |

For $J_x f$, see [[Linear approximation]]. 

==== Discussion ====
This definition does nothing more than emphasizing the functionality of $L_x^f$ in $f$.

=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Derivative_of_a_function|Derivative of a function]], [[http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative|Fréchet derivative]]
==== Parents ====
=== Context ===
[[Linear approximation]]