Найти производную функции $f(x) = \sin(\sqrt{x})$.

$u=\sqrt x$, $u' = \dfrac{1}{2\sqrt x}$. $$ f'(x) = \cos(u)\cdot u' = \frac{\cos(\sqrt x)}{2\sqrt x}. $$

$$ \boxed{f'(x) = \dfrac{\cos(\sqrt x)}{2\sqrt x}} $$