Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 1 / 3 / b / Solution

Differentiate each coordinate with respect to the parameter $t$ and use the chain rule:Both coordinates are defined where $\sin t\ne 0$ and $\cos t\ne 0$. As a check, $xy=1$ there, so the same derivative is $-1/x^2$.