Let $X$ be a vector field, $M$ be a smooth surface and $v \in T_p M $ and a curve $γ :I \rightarrow M$ s.t. $γ(0)=p, γ'(0)=v$
then we can define the "derivative" of $X$ as $\frac{d}{dt}(X\circ γ)|_{t=0 }$
I don't understand this definition, what we mean by $(X\circ γ)$ ?
For instance, take $M=S^2, $ $X(t)=(-\text{sin}t,\text{cos}t,0)$ and $γ(t)=(\text{cos}t,\text{sin}t,0)$ what $(X\circ γ)$ means ?