# Just try to post my first problem

Calculus Level 1

For each positive integer $n$, let

$f^n (x) = \sin ( f^{n-1} (x) ),$

with $f^0 (x) = x$.

Let $y(x) = \lim_{n \rightarrow \infty } f^n(x)$.

Determine $y'(0)$.

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