Understanding Schutz's Geodesic Deviation Eq. 6.84

[patrik1982]

I have some problem understanding the section on "Geodesic deviation" in schutz, more specifically I'm confused by eq. 6.84:

Eq 6.84 reads (ξ is the 'connecting vector' from one geodesic to Another, V is the tangent vector):

We can use (6.48) to obtain
∇_V∇_Vξ^α = ∇_V(∇_Vξ^α) = (d/dλ)(∇_Vξ^α) = Γ^α_β0(∇_Vξ^α)

(Eq 6.48 gives the second equality, but I fail to see why the last equality is true)​

Eq 6.48 says the following:
U^βV^α_;β = 0 ⇔ (d/dλ)V = ∇_UV = 0
(U is tangent to the curve, λ is the parameter along it)Can someone please help me and explain what's going on?

 

[martinbn]

In the book it is

##\nabla_V(\nabla_V\xi^\alpha)=\frac{d}{d\lambda}(\nabla_V\xi^\alpha)+\Gamma^\alpha_{\beta 0}(\nabla_V\xi^\beta)##

 

[patrik1982]

In the book it is

##\nabla_V(\nabla_V\xi^\alpha)=\frac{d}{d\lambda}(\nabla_V\xi^\alpha)+\Gamma^\alpha_{\beta 0}(\nabla_V\xi^\beta)##

Nope. At least not in my book. (Photo attached)
So, this is a misprint then?

 

[RockyMarciano]

Nope. At least not in my book. (Photo attached)
So, this is a misprint then?

No, the relaevant equation, equivalent to the one martinbn wrote, is the next one:6.85