So I've started reading Landau's classical mechanics text and I'm at the part where L(v'(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}) = L(v^{2}+ 2v⋅ε +ε^{2}) and he says to expand it out in powers of ε to get L(v'^{2}) = L(v^{2}) + ∂L/∂(v^{2}) * 2v⋅ε where v and ε are vectors.

Can someone explain how this result is obtained in more detail?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Expanding a multivariable function in powers of one of the variables?

**Physics Forums | Science Articles, Homework Help, Discussion**