Let $f(x) = x - 5$. If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) = .....$

If $f(x)=\cosh ^{-1}\left(\frac{1-x}{1+x}\right)$ is well defined, then $f^{\prime}(x)=$

Find the value of $k$ if $\frac{d}{d x}\left\{\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2 \cos (4 x)}}}}\right\} = k \sec \left(\frac{x}{2}\right) \tan \left(\frac{x}{2}\right)$

If $f(x) = \log_{x^2} (\ln x)$,then $f'(e)$ is equal to . . . . . .

$\frac{d}{dx}\left( \frac{\cot^2 x - 1}{\cot^2 x + 1} \right) = $

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