Question

Let $M$ be $C^{\infty}$-manifold and $(U,\phi)$ be local chart with $x\in U$ where $\phi =(x_1, \dots,x_n)$. For $X\in (T_k^rM)_x:=J_0^r(\mathbb{R}^k,M)_x$, can the jet $X$ be represented by the local chart like a tangent vector? And if it can be, how do we represent it?