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

[Summetros]

So I've started reading Landau's classical mechanics text and I'm at the part where L(v'²) = L(v² + 2v⋅ε +ε²) and he says to expand it out in powers of ε to get L(v'²) = L(v²) + ∂L/∂(v²) * 2v⋅ε where v and ε are vectors.

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

 

[Summetros]

Never mind, I found an explanation on physics.stackexchange.com.

http://physics.stackexchange.com/qu...ticles-kinetic-energy-expansion-of-a-function