  We show that for any $k$-times continuously differentiable function
$f:[a,\infty)\longrightarrow{\mathbb R}$, any integer $q\ge 0$ and any
$\alpha>1$ the inequality $$\liminf_{x\to\infty} \frac{x^k \cdot\log x\cdot
\log_2 x\cdot\dots\cdot
  \log_q x \cdot f^{(k)}(x)}{1+|f(x)|^\alpha}\le 0 $$ holds.
