Let $n \in \mathbb{N}_0$, and let $\mathcal{P}_n$ denote the complex [vector space](/page/Vector%20Space) of algebraic polynomials $p: \mathbb{C} \to \mathbb{C}$ of degree at most $n$. For every $p \in \mathcal{P}_n$ and every $x \in (-1,1)$,
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\begin{align*}
\sqrt{1 - x^2}\, |p'(x)| \leq n \|p\|_{L^\infty([-1,1])}.
\end{align*}