content_image/300353.jpg content_image/300354.jpg content_image/300352.jpg content_image/300351.jpg content_image/300350.jpg
and t ∈$_{R}$ sufficiently close to zero, we have that 

<img src='content_image/300353.jpg'>

Proof. Let H$_{t}$ ( o ) ≜ 1 + th$_{1}$ ( o ) + t $^{2}$h$_{2}$ ( o ) and ˙ H$_{t}$ ( o ) ≜ h$_{1}$ ( o ) + 2 th$_{2}$ ( o ). 

<img src='content_image/300354.jpg'>

We will pass the derivative inside the integral using (S2) and apply the product rule. The first term we need to consider is 

<img src='content_image/300352.jpg'>

The second is 

<img src='content_image/300351.jpg'>

Returning to (A.6), this shows that d 2 dt $_{2}$Φ $^{T U}$( P$_{t}$ ) ∣ ∣ t =0 is equal to 

<img src='content_image/300350.jpg'>

