HMMT 2004 K4

Calculus
Answer

Let $f(x)=\cos (\cos (\cos (\cos (\cos (\cos (\cos (\cos x)))))))$ , and suppose that the number $a$ satisfies the equation $a=\cos a$ . Express $f^{\prime}(a)$ as a polynomial in $a$ .

Dataset text NuminaMath olympiads. Quoted with source.

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a^{8}-4 a^{6}+6 a^{4}-4 a^{2}+1

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