Calculus of Variations

c299792458

Hi, why is it true that for [tex]\vec{x^\varepsilon}=\frac{\vec{x(t)}-\varepsilon \vec{y(t)}}{|\vec{x(t)}-\varepsilon \vec{y(t)}|}[/tex],

[tex]\frac{\partial}{\partial x} |\vec{\dot{x}}|^2=-2 |\vec{\dot{x}}|^2 \vec{x}[/tex] at [tex]\varepsilon[/tex]=0?
Thanks.