Bernstein's Inequality

Let $P$ be a Polynomial of degree $n$ with derivative $P'$. Then

$$\vert\vert P'\vert\vert _\infty\leq n \vert\vert P\vert\vert _\infty,$$

where

$$\vert\vert P\vert\vert _\infty \equiv \max_{\vert z\vert=1} \vert P(z)\vert.$$