Just try to post my first problem

Calculus Level 1

For each positive integer nn, let

fn(x)=sin(fn1(x)), f^n (x) = \sin ( f^{n-1} (x) ),

with f0(x)=x f^0 (x) = x .

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

Determine y(0) y'(0) .

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