Solution:
\( y^\prime =3 \left ( e^{ \sin (\frac{t}{2} )} \right ) ^2 \left ( e^{ \sin (\frac{t}{2} )} \right ) \cos \left ( \frac{t}{2} \right ) \frac{1}{2}=\frac{3}{2} \left ( e^{ \sin (\frac{t}{2} )} \right ) ^3 \cos \left ( \frac{t}{2} \right ) \)
