Answer
$\frac{ds}{dt} = \frac{3 \pi}{2}(cos(\frac{3 \pi t}{2}) -sin (\frac{3 \pi t}{2}))$
Work Step by Step
$s = sin(u) + cos(u)$
where,
$u = \frac{3 \pi t}{2}$
Now,
$\frac{ds}{du} = cos(u) -sin (u)$
and,
$\frac{du}{dt} = \frac{3 \pi}{2}$
So,
$\frac{ds}{dt} = \frac{ds}{du} \times \frac{du}{dt}$
$\frac{ds}{dt} = \frac{3 \pi}{2}(cos(u) -sin (u))$
$\frac{ds}{dt} = \frac{3 \pi}{2}(cos(\frac{3 \pi t}{2}) -sin (\frac{3 \pi t}{2}))$
