Answer
$\frac{dy}{dt}$ = $\frac{-tsin(t^{2})}{\sqrt {(1+cos(t^{2})}}$
Work Step by Step
$y$ = $\sqrt {(1+cos(t^{2})}$
$\frac{dy}{dt}$ = $\frac{d}{dt}$$\sqrt {(1+cos(t^{2})}$
$\frac{dy}{dt}$ = $\frac{1}{2\sqrt {(1+cos(t^{2})}}$ $\frac{d}{dt}$$(1+cos(t^{2}))$
$\frac{dy}{dt}$ = $\frac{1}{2\sqrt {(1+cos(t^{2})}}$ $(-sin(t^{2}))$ $\frac{d}{dt}$$(t^{2})$
$\frac{dy}{dt}$ = $\frac{1}{2\sqrt {(1+cos(t^{2})}}$ $(-sin(t^{2}))$$(2t)$
$\frac{dy}{dt}$ = $\frac{-tsin(t^{2})}{\sqrt {(1+cos(t^{2})}}$
