Question

let $(M,g)$ be a Riemannian manifold. and Define the exponential map by $exp : TM \rightarrow M ,exp(x,v) = \gamma(1)$ where $\gamma$ is the geodesic with $\gamma (0) = x$ and $d/dt_{t=0} \gamma = v$ and $v$ sufficiently small. My question is: what is the differential of exp in some point $exp_{\star,(x,v)} : T_{(x,v)}(TM) \rightarrow TM$ ?