  Let $f$ be a holomorphic cusp form of weight $k$ with respect to full modular
group $SL_2(\mathbb{Z})$ satisfying a normalized Hecke eigenform, $L_f(s)$ the
$L$-function attached to the form $f$. Good gave the approximate functional
equation and mean square formula of $L_f(s)$. In this paper, we shall
generalize these formulas for the derivatives of $L_f(s)$.
