  We consider functions of the type $f(z)=z+a_2z^2+a_3z^3+\cdots$ from a family
of all analytic and univalent functions in the unit disk. Let $F$ be the
inverse function of $f$, given by $F(z)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on
some $|w|\le r_0(f)$. In this paper, we find the sharp bounds of $\big |
|A_{n+1}|-|A_n|\big |$, for $n=1,\,2$, for some subclasses of univalent
functions.
