Question about flow

Question

Could anyone explain to me how to get to equation 1.15 from 1.14?

Answer 1

If just expresses the fact that, for differentiable $f$, $$f(t) = f(0) + tf^\prime(0) + \cal{O} (t^2)$$ (think of $\sigma_t(p)$ as a function of $t$).