Answer
$$y'=\frac{x\cos(1+x^2)}{\sqrt{\sin(1+x^2)}}$$
Work Step by Step
$$y'=(\sqrt{\sin(1+x^2})'=\frac{1}{2\sqrt{\sin(1+x^2)}}(\sin(1+x^2))'=\frac{1}{2\sqrt{\sin(1+x^2)}}\cos(1+x^2)(1+x^2)'=
\frac{1}{2\sqrt{\sin(1+x^2)}}\cos(1+x^2)\cdot2x=
\frac{x\cos(1+x^2)}{\sqrt{\sin(1+x^2)}}$$
