Multi Variable Differentiation
Overview
Total Derivative Definition
a multi-variable function
{% f(x_1,x_2,...,x_n) %}
is said to differentiable if there exists a
linear transformation
{% T_a : \mathbb{R}^n \rightarrow \mathbb{R} %}
and a scalar function
E(a,v) such that
{% f(\vec{a} + \vec{v}) = f(\vec{a}) + T_a(\vec{v}) + |\vec{v}| \times E(\vec{a},\vec{v}) %}
where
{% E(\vec{a},\vec{v}) \rightarrow 0 %}
as
{% |\vec{v}| \rightarrow 0 %}
