Let's be specific and use a simpler example than what I actually need to solve.
$$
\begin{split}
x(t) &= t + A\sin(wt) \\
y(t) &= B \cos(wt)
\end{split}
$$
How would I obtain the derivative of x in y? My maths are pretty rusty :(

I'd like to be able to derive Gerstner wave normal equations by myself, and that would help. Any good book I could find the answer in (the theory) would also be welcome!