
push forward
show that $\displaystyle (\phi\circ\gamma)^{\prime}(t)=\phi_{*}(\gamma^{\pr ime}(t))$
where if $\displaystyle v\in T_pM$ is a tangent vector and $\displaystyle \phi:M\rightarrow N$ is a smooth function and we define
$\displaystyle (\phi_{*}v)(f)=v(f\circ\phi)$
$\displaystyle \gamma$ is a curve on $\displaystyle M$
$\displaystyle f:N\rightarrow \mathbb{R}$
(Pushing forward)

Uh, just insert the definitions, remembering perhaps that $\displaystyle \gamma'(t)(f) = {\mathrm{d}f(\gamma(t))\over \mathrm{d}t}\Big_{t=t}$.

thank you, I did figure it out. Forgot about that definition