Answer
$$y'=\cos(t+\cos\sqrt t)(1-\frac{1}{2\sqrt t}\sin\sqrt t)$$
Work Step by Step
$$y'=(\sin(t+\cos\sqrt t))'=\cos(t+\cos\sqrt t)(t+\cos\sqrt t)'=
\cos(t+\cos \sqrt t)(1+(-\sin\sqrt t)(\sqrt t)')=
\cos(t+\cos\sqrt t)(1-\frac{1}{2\sqrt t}\sin\sqrt t)$$
