If $f(x) = \begin{cases} 1, & x < 0 \\ 1 + \sin x, & 0 \le x < \frac{\pi}{2} \end{cases}$,then $f'(0) = $

Let $[x]$ denote the greatest integer less than or equal to $x$. Then the number of points where the function $y = [x] + |1 - x|$ for $-1 \leq x \leq 3$ is not differentiable,is

Let $f(x) = \begin{cases} 1, & \forall x < 0 \\ 1 + \sin x, & \forall 0 \le x \le \pi/2 \end{cases}$,then what is the value of $f'(x)$ at $x = 0$?

Let $a \in Z$ and $[t]$ be the greatest integer $\leq t$. Then the number of points,where the function $f(x) = [a + 13 \sin x], x \in (0, \pi)$ is not differentiable,is $........$.

The function defined by $f(x) = \max \{x^2, (x - 1)^2, 2x(1 - x)\}$ for $0 \le x \le 1$:

The derivative of $y = 1 - |x|$ at $x = 0$ is