= Bernstein inequality for algebraic polynomials
{c}
{title2=$|p'(x)|\le n\|p\|_{[-1,1]}/\sqrt{1-x^2}$}
For a polynomial of degree at most $n$, this <derivative> estimate holds for $-1<x<1$. It controls the derivative away from the endpoints. Sampling it at <Chebyshev polynomial> roots supplies the hypotheses of the <Chebyshev nodal derivative comparison>, which controls the missing endpoint regions. The norm is taken on the entire interval, although the displayed pointwise bound concerns its interior.
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