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 $y'(0)$ .