2024 SJI P2 Q4

The functions f and g are defined as follows:

\[\mathrm f(x)=\sin\left(\frac{x-\pi}3\right),\quad-\pi\leq x<2\pi\quad\text{and}\quad\mathrm g(x)=x^3+1,\quad x\in\mathbb R.\]

1. Find an expression for \(\dfrac{\mathrm d}{\mathrm dx}\left[(\mathrm g\circ\mathrm f)\left(\dfrac1x\right)\right]\).[4]
2. Find an expression for \(\dfrac{\mathrm d}{\mathrm dx}[\mathrm f(x)\times\mathrm g(x)]\).[3]