If $y=x \log \left(\frac{1}{a x}+\frac{1}{a}\right)$,then $x(x+1) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=$

For $n \in \mathbb{N}$,find the $n$-th derivative of $\log x$,i.e.,$\frac{d^{n}}{d x^{n}}(\log x) = $

If $y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log _e x}{1-6 \log _e x}\right]$, then $\frac{d^2 y}{d x^2}=$

If $f(x) = \frac{x^2}{x+a}$,then $f^{\prime \prime}(a)$ is equal to

If $y=3 \cos (\log x)+4 \sin (\log x)$,then $x^2 y_2+x y_1=$

If $y = \operatorname{Sec}^{-1} x$, then $\frac{d^2 y}{d x^2} = $