Calculate the normal vector of $c(t)=\exp_{\gamma(t)} sV(t)$?

Question

For a 2-dimensional Riemannian manifold $(M,g)$, $\gamma:[0,a]\rightarrow M$ is a closed simple curve, and $V(t)$ is a vector field along $\gamma(t)$. Assume $$ f(s,t)= \exp_{\gamma(t)} sV(t) ~~~~~~s\in(-\epsilon,\epsilon),~~~t\in[0,a] \tag{1} $$ Then, for fixed $s\in(-\epsilon,\epsilon)$, how to calculate the normal vector of the curve $f_s(t)=f(s,t)$ ?