If $f(x)=\frac{2x}{4+3|x|}, x \in R$, then $f^{\prime}(0)=$

Let $f:[-1,1] \rightarrow R$ be a function defined by $f(x)=\begin{cases} x^2 \left| \cos \left(\frac{\pi}{x}\right) \right| & \text{for } x \neq 0 \\ 0 & \text{for } x=0 \end{cases}$. The set of points where $f$ is not differentiable is

Which of the following statements is not true?

Assertion $(A)$: If $y = f(x) = (|x| - |x - 1|)^2$,then $\left(\frac{dy}{dx}\right)_{x=1} = 1$.
Reason $(R)$: If $\lim_{x \rightarrow a} \frac{f(x) - f(a)}{x - a}$ exists,then it is called the derivative of $f(x)$ at $x = a$.
Then:

Let $f(x)=a_0+a_1|x|+a_2|x|^2+a_3|x|^3$, where $a_0, a_1, a_2, a_3$ are real constants. Then $f(x)$ is differentiable at $x=0$ if and only if:

If $f(x) = \begin{cases} ax^2 + b; & x \le 0 \\ x^2; & x > 0 \end{cases}$ possesses a derivative at $x = 0$,then: