A Partial Differential Equation

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!

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How might one solve this? –  TheBluegrassMathematician Apr 28 '14 at 2:34