If $$x \neq 0$$ and $$f(x)$$ satisfies $$8 f(x)+6 f(1 / x) =x+5$$, then $$\frac{d}{d x}\left(x^2 f(x)\right)$$ at $$x=1$$ is

If $$f(x)=\cot ^{-1}\left(\frac{x^x+x^{-x}}{2}\right)$$, then $$f^{\prime}(1)=$$

If $$x=\sec \theta-\cos \theta$$ and $$y=\sec ^n \theta-\cos ^n \theta$$, then $$\left(x^2+4\right)\left(\frac{d y}{d x}\right)^2$$ is equal to

If $$y=\log _{\cot x} \tan x-\log _{\tan x} \cot x +\tan ^{-1}\left(\frac{4 x}{4-x^2}\right)$$, then $$\frac{d y}{d x}$$ is equal to