Suppose $f(x)=\sin{x}$, and let $k$ be a real number. Let $F(x)=f(x^k)$ and $G(x)=[f(x)]^k$.
Find expressions for (a) $F'(x)$ and (b) $G'(x)$.
(a) $F'(x)=$
(b) $G'(x)=$