Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 5 / a / Solution

The coordinate sum is $2\sin t$, while the sum of their cubes is $6\sin t-4{\sin }^{3}t$. Along the parametrized curve, the composite function is therefore $-3\sin t/2-{\sin }^{3}t/3$. Differentiate, or apply the multivariable chain rule, to obtain