If $f(x) = x(\sqrt{x} - \sqrt{x + 1}),$ then

If $f(x) = \begin{cases} \frac{x-1}{2x^2-7x+5}, & \text{for } x \neq 1 \\ -\frac{1}{3}, & \text{for } x=1 \end{cases}$,then $f^{\prime}(1)$ is equal to:

If $y = \sec^{-1} \left( \frac{2x}{1 + x^2} \right) + \sin^{-1} \left( \frac{x - 1}{x + 1} \right)$,then $\frac{dy}{dx}$ is equal to

For the function $f(x) = e^{\sin |x|} - |x|$, $x \in R$, consider the following statements:
Statement $I$: $f$ is differentiable for all $x \in R$.
Statement $II$: $f$ is increasing in $(-\pi, -\frac{\pi}{2})$.
In the light of the above statements, choose the correct answer from the options given below:

The function $f(x) = \sin^{-1}(3x - 4x^3)$ is

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