y(t)=(3/2)*sin(12*pi*t)
y't=(3/2)*cos(12*pi*t)
Is that correct?
Hmmm... There is a confusion... Pardon me if it is my fault
Get back to my formula.
$\displaystyle g(t)=12 \pi t \implies g'(t)=12 \pi$
$\displaystyle f(x)=\sin(x) \implies f'(x)=\cos(x)$
So the formula give :
$\displaystyle y'(t)=\frac 32 \cdot [f(g(t))]'=\frac 32 \cdot g'(t) \cdot f'(g(t))=\frac 32 \cdot 12 \pi \cdot \cos(12 \pi t)=\dots$