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 $$f(x)=2x^2+3x-5$$, then the value of $$f'(0)+3f'(-1)$$ is equal to

If $$y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)$$ and $$x \neq 0$$. When $$x=-1, \frac{d y}{d x}$$ is equal to