Let $y = \log_e \left(\frac{a + b \sin x}{a - b \sin x}\right)$, then value of $\frac{dy}{dx}$ is :

If the function $f(x) = \begin{cases}\frac{\sin 3x}{x}, & \text{if } x \neq 0\\ \frac{3k}{2}, & \text{if } x = 0\end{cases}$ is continuous at $x = 0$, then the value of $k$ is

If

$f(x) = \begin{cases}\frac{1- \tan x}{4x-\pi}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4}\end{cases}$

is continuous at $x = \frac{\pi}{4}$, then the value of k is

If $y = x\sin y$, then $\frac{dy}{dx}$ is:

The derivative of $|x|$ with respect to $x$, where $x \in R \sim \{0\}$ is

If $x = a\left(t - \dfrac{1}{t}\right)$, $y = b\left(t + \dfrac{1}{t}\right)$, then $\dfrac{dy}{dx} =$

If $y = \frac{1}{\sqrt[3]{1-x^3}}$ then $\frac{dy}{dx}$ is equal to