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

If $f(x) = \cos x\,\cos 2x\,\cos 4x\,\cos 8x\,\cos 16x$, then $f'\left(\dfrac{\pi}{4}\right) =$

If $y = \dfrac{1}{3x + 5}$, then the value of $\dfrac{d^9 y}{dx^9}$ is..

The derivative of $\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right)$ with respect to $\tan^{-1}\left(\dfrac{x}{\sqrt{1 - x^2}}\right)$ at $x = \dfrac{1}{2}$ is