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2008th Derivative of Trig

Source: HMMT 2008 Calculus Problem 5

March 2, 2008
calculusderivativetrigonometrycalculus computations

Problem Statement

(4) Let f(x) \equal{} \sin^6\left(\frac {x}{4}\right) \plus{} \cos^6\left(\frac {x}{4}\right) for all real numbers x x. Determine f(2008)(0) f^{(2008)}(0) (i.e., f f differentiated 2008 2008 times and then evaluated at x \equal{} 0).