What is $\frac{\partial F}{\partial y}$ evaluated at $\varepsilon=0$ for
$F=\|\vec{\dot{y^\varepsilon}}\|^2$ where $\vec{y^\varepsilon}=\frac{\vec{y(x)}-\varepsilon \vec{\eta(x)}}{\|\vec{y(x)}-\varepsilon \vec{\eta(x)}\|}$ and $\vec{\eta(x)}$ is smooth?
Thanks!