How to solve the problem based on vector triple product

Question

I m stuck by this problem. I know the formula but I can't solve this problem.

Plz help me

Answer 1

Let $n \geq 1$ be an integer. By the derivative of a function $f: \mathbb{R} \to \mathbb{R}^{n}$ we mean the function $x \mapsto (f_{1}'(x), \dots, f_{n}'(x))$, where $f'_{i}$ denotes the derivative of the $i$th component $f_{i}: \mathbb{R} \to \mathbb{R}$ of $f$ for each $1 \leq i \leq n$.

Note that the function $\theta \mapsto a \times (b \times c)$ takes $\mathbb{R}$ (for example) to be a subset of $\mathbb{R}^{3}$, so once you get the cross products then you get the derivative of the function.