The professor gave this formula without providing a proof. I would like to know how this can be derived.
Let $X$ be a vector field, $w$ be a $p$-form. Then, $$L_X w(v_1,v_2,\ldots,v_p)=X(w(v_1,v_2,\ldots,v_p))-\sum_{i=1}^p w(v_1,\ldots,L_Xv_i,\ldots,v_p).$$
The definition for the Lie derivative is given by
$$L_Xw = \left.{{d}\over {dt}}\right|_{t=0} \phi_t^*w$$
where $\phi_t$ is the one parameter diffeomorphism group generated by $X$, and $\phi_t^*$ denotes the pull back.
Thank you guys in advance for any answers and hints.