Differentiating Cosines with Cosines?

Calculus Level 5

[dd(cosx)(n=1100cosnx)]x=2π=? \large \left[ \frac { d }{ d\left( \cos { x } \right) } \left( \sum _{ n=1 }^{ 100 }{ \cos { nx } } \right) \right] _{ { x=2\pi }} =\, ?

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