Finding a curve in S^n whose velocity vector is a given vector

Question

I want to to prove $T_x(S^n)=\{y\in \mathbb{R}^{n+1}|<x,y>=0\}$. For that I want to find a curve in $S^n$ whose velocity vector is a given vector, i.e., if $y\in \mathbb{R}^{n+1}$ then I should find a curve $\gamma:(-\epsilon,\epsilon)\to S^n$ such that $\gamma(0)=x$ and $\gamma^{'}(0)=y$. Can you please help to find this.