The differential coefficient of the function $|x - 1| + |x - 3|$ at the point $x = 2$ is

$\frac{d}{dx}\sqrt{\sec^2 x + \text{cosec}^2 x} = $

Compute the derivative of $g(x) = \cot x$.

If $y=\frac{\cos x}{1+\sin x}$,then
$(a)$ $\frac{dy}{dx}=\frac{-1}{1+\sin x}$
$(b)$ $\frac{dy}{dx}=\frac{1}{1+\sin x}$
$(c)$ $\frac{dy}{dx}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)$
$(d)$ $\frac{dy}{dx}=\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)$

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $(ax^{2} + \sin x)(p + q \cos x)$

Let $f(x + y) = f(x) + f(y)$ and $f(x) = x^2 g(x)$ for all $x, y \in R$,where $g(x)$ is a continuous function. Then $f'(x)$ is equal to