# Calculus of Variations

by c299792458
Tags: calculus, variations
 P: 71 Hi, why is it true that for $$\vec{x^\varepsilon}=\frac{\vec{x(t)}-\varepsilon \vec{y(t)}}{|\vec{x(t)}-\varepsilon \vec{y(t)}|}$$, $$\frac{\partial}{\partial x} |\vec{\dot{x}}|^2=-2 |\vec{\dot{x}}|^2 \vec{x}$$ at $$\varepsilon$$=0? Thanks.