Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $f(0)=1$ and $|f(x)-f(y)| \leq\left|\sin \left\{(x-y)^2\right\}\right| \text { for all } x, y \in \mathbb{R}$ and let $g$ be the function defined by $g(x)=x^2 f\left(x^2\right)$ for all $x \in \mathbb{R}$. Then the value of $g^{\prime}(2)$ is

• A

  $2$
• Correct answer
  B

  $4$
• C

  $6$
• D

  $0$

Hence, the correct answer is option: 'B'.