I'm not sure if I did this correctly.

s(t)= √(t^2 + 2t)

s'(t)= (t + 1)/[√(t^2 + 2t)]

Here's where I have trouble:

s''(t)= (t^2 + 2t)^(-1/2) (t + 1)

= (-1/2)(t^2 + 2t)^(-3/2) (t + 1) + (t^2 + 2t)^(-1/2) (1)

= 1/[√(t^2 + 2t)] - (t+1)/[2(t^2 + 2t)^(3/2)]

Is this the correct answer?