$\frac{d}{dx}({x^2} + \cos x)^4 = $

Let $f$ and $g$ be two differentiable functions on $R$ such that $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$. Then for all $x$,which of the following is true?

For the differentiable function $f: R - \{0\} \rightarrow R$,let $3 f(x) + 2 f\left(\frac{1}{x}\right) = \frac{1}{x} - 10$. Then $\left|f(3) + f^{\prime}\left(\frac{1}{4}\right)\right|$ is equal to

If $f(x) = \cos^{-1} x$,$g(x) = e^x$,and $h(x) = g(f(x))$,then $\frac{h'(x)}{h(x)} = $

If $f^{\prime}(x)=\tan^{-1}(\sec x+\tan x)$ for $-\frac{\pi}{2} < x < \frac{\pi}{2}$ and $f(0)=0$,then $f(1)$ is equal to:

Find the derivative of the following function: $\operatorname{cosec} x \cot x$.