#### Answer

$y' = -5sin(5t)$

#### Work Step by Step

$y = cos(5t)$
$y' = (cos(5t))'$
The inner function is $g(t) = 5t$
and the outer function is $f(u) = cos (u)$
$f'(u) = -sin (u)$
$y' = (cos(5t))' = - sin (g(t))\times g'(t) = -sin (5t)\times5 = -5sin(5t)$