If $x=3 \cos t$ and $y=4 \sin t$,then $\frac{d^2 y}{d x^2}$ at the point $(x_0, y_0)=(\frac{3}{2} \sqrt{2}, 2 \sqrt{2})$ is

If $y = \log(\cosh x)$,then $\frac{d^2 y}{d x^2} = $

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$,then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to

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:

If $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$,then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

If $y^2 = a x^2 + 2 x + c$,then $y^3 \frac{d^2 y}{d x^2}$ is