Answer
$\frac{dy}{dt}$ = $-7(1+cos^{2}(7t))^{2}$$[cos(7t)sin(7t)]$
Work Step by Step
$y$ = $\frac{1}{6}$$(1+cos^{2}(7t))^{3}$
$\frac{dy}{dt}$ = $\frac{d}{dt}$$\frac{1}{6}$$(1+cos^{2}(7t))^{3}$
$\frac{dy}{dt}$ = $\frac{3}{6}$$(1+cos^{2}(7t))^{2}$ $\frac{d}{dt}$$(1+cos^{2}(7t))$
$\frac{dy}{dt}$ = $\frac{3}{6}$$(1+cos^{2}(7t))^{2}$$[2cos(7t)]$ $\frac{d}{dt}$$cos(7t)$
$\frac{dy}{dt}$ = $\frac{3}{6}$$(1+cos^{2}(7t))^{2}$$[2cos(7t)]$$[-sin(7t)]$ $\frac{d}{dt}$$(7t)$
$\frac{dy}{dt}$ = $\frac{3}{6}$$(1+cos^{2}(7t))^{2}$$[2cos(7t)]$$[-sin(7t)]$$(7)$
$\frac{dy}{dt}$ = $-7(1+cos^{2}(7t))^{2}$$[cos(7t)sin(7t)]$
