If $y = A \cos(nx) + B \sin(nx)$,then $\frac{d^2y}{dx^2} = $

If the three functions $f(x)$,$g(x)$,and $h(x)$ are such that $h(x) = f(x) \cdot g(x)$ and $f^{\prime}(x) \cdot g^{\prime}(x) = c$,where $c$ is a constant,then $\frac{f^{\prime \prime}(x)}{f(x)} + \frac{g^{\prime \prime}(x)}{g(x)} + \frac{2c}{f(x) \cdot g(x)}$ is equal to:

The function $y=e^{kx}$ satisfies $(\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}$. It is valid for

If $x = \log p$ and $y = \frac{1}{p}$,then

If $y=\tan \left(3 \tan ^{-1} x\right)$,then $\left(1-3 x^2\right) \frac{d^2 y}{d x^2}-12 x \frac{d y}{d x}=$

If $y = \log_e(\log_e x)$ for $x > 1$,then $\frac{d^2 y}{dx^2} = $ . . . . . . .