\(\displaystyle

\dfrac{s(t)\cdot s^{(1)}(\dfrac{t}{2})\cdot \dotsc \cdot s^{(n+1)}(\dfrac{t}{n+1})}{

s(t)\cdot s^{(1)}(\dfrac{t}{2})\cdot \dotsc \cdot s^{(n)}(\dfrac{t}{n})}=s^{(n+1)}(\dfrac{t}{n+1})=1/n

\).

\(\displaystyle s(\dfrac{t}{1+n})=\dfrac{t^{n+1}}{n}\).

\(\displaystyle s(t)=\dfrac{(tn+n)^{n+1}}{n}\).