The pushforward of a map $F:M \to N$ at a point $P \in M$ is defined as $F_*:T_P(M) \to T_{F(P)}(N)$ where $(F_*X)(f) = X(f \circ F)$
where $X \in T_P(M)$.
The differential of a function $f$ defined on $M$ at $P$ is $df_P(X_P) = X_Pf.$
What is the relation? How to show that the differential is got from the pushforward definition? Presumable for the differential case, $f:M \to \mathbb{R}$, but I can't get the answer.