I don't get it. Why there's [tex]\frac{\partial L}{\partial v^2}[/tex]? If we expand function in Taylor series (taking [tex]\vec{\epsilon}[/tex] as an independent variable) there should be only derivatives in respect to that var (epsilon).
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I think I got it  from mean value theorem we have: [tex]\frac{f(x+h)  f(x)}{h} \approx f'(x), h \to 0[/tex], so: [tex]L( (v+\epsilon)^2 ) \approx L (v^2) + \frac{\partial L (v^2)}{\partial v^2} (v^2)' \epsilon[/tex] :)
