Let $M$ be a differentiable manifold and $f$ a differentiable mapping
$f : (-\epsilon, \epsilon) \times M \to M$, $f(t,x) = f_t(x)$
Furthermore let $\gamma: (-\epsilon,\epsilon) \to M$ be a differentiable curve through $p \in M$.
My question is: Is there a formula for $\frac{d}{dt} \vert_{t=0} f_t(\gamma(t))$ ?
Thanks in advance!