If $g(x) = (x^2 + 2x + 1) \cdot f(x)$ such that $f(0) = 5$ and $\lim_{x \to 0} \frac{f(x) - 5}{x} = 4$, then $g'(0) = $

$\frac{d}{d x}\left(\sqrt{\frac{1-\tan x}{1+\tan x}}\right) = $

If $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

The derivative of $\cosh^{-1} x$ with respect to $\log x$ at $x=5$ is

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