Overview
Given an operator {% O %} from Banach Spaces {% U %} and {% V %}
{% O:U \rightarrow V %}
and elements of {% U %} labeled {% x %} and {% t %}, the
Gateaux Derivative {% D %} is an
operator
defined by
{% \lim_{\epsilon \to 0} || \frac{O(x+\epsilon t) - O(x)}{\epsilon} - D O(x)t || = 0 %}
see Siddiqi