On a method of obtaining of an analogue of V. A. Markof enequality for polynomials in metric $L^p(0, 1), 1<p<\infty$

For any polynomial $P_n(x)$ of degree $n$ a new method of estimation of $| P_n^{(s)}(x)|$ in arbitrary point $x\in[0, 1], 0\leq s\leq n$ has been presented. It has been proved that the obtained estimates are not less exact compared with other methods.