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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