Solution
= Solution
The coordinate sum is $2\sin t$, while the sum of their cubes is $6\sin t-4\sin^3t$. Along the <parametrized curve>, the composite <function> is therefore $-3\sin t/2-\sin^3t/3$. Differentiate, or apply the multivariable <chain rule>, to obtain
$$
\boxed{\frac{\mathrm d f(x(t),y(t))}{\mathrm dt}=-\cos t\left(\frac32+\sin^2t\right).}
$$