 Solution

ID: 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

\frac{d f ( x ( t ) , y ( t ))}{d t} = - cos t (\frac{3}{2} + sin^{2} t) .

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