Seventy deadly sines

Calculus Level 3

f(x)=sinsin...sin70 sines(x).f(x)=\overbrace{\sin\sin ... \sin}^{70\text{ sines}} (x).

Calculate the seventh derivative of ff evaluated at x=0.x=0.

Note: Using computer software to answer this question is an even deadlier sin than nesting 70 sines inside each other, so don't do it.

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