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

Let $S$ be the set of all points in $(-\pi, \pi)$ at which the function $f(x) = \min\{\sin x, \cos x\}$ is non-differentiable. Then $S$ is a subset of which of the following?

The domain of the derivative of the function $f(x) = \frac{x}{1+|x|}$ is

The left-hand derivative of $f(x) = [x]\sin(\pi x)$ at $x = k$,where $k$ is an integer and $[x]$ denotes the greatest integer function $\le x$,is:

The function which is continuous for all real values of $x$ and differentiable at $x = 0$ is

Assertion $(A)$: $f(x) = |x|$ is differentiable at $x = a \neq 0$ and continuous but not differentiable at $x = 0$.
Reason $(R)$: If a function is differentiable at a point,then it is continuous at the point. But the converse is not true.