Let $X,Y\in \mathfrak{X}(M)$ and $\Phi_{t}^{X}$ an integral curve of $X$. Show that $\frac{d}{dt}Y(m)(f\circ \Phi_{t}^{X}) =Y(m)(Xf).$

Question

Let $M$ be a manifold, $X,Y\in \mathfrak{X}(M)$. Let $\Phi_{t}^{X}$ an integral curve or flow line of $X$. We define $$\begin{array}{rcl} Xf:M &\rightarrow & \mathbb{R} \\ m &\rightarrow & X(m)(f) \end{array}$$

for all $f\in C^{\infty}(M)$. Show that $$\frac{d}{dt}Y(m)(f\circ \Phi_{t}^{X}) =Y(m)(Xf)$$ for any $m \in M$.

Remark: I tried but I'm very confused.