If $y=2 x^{n+1}+\frac{3}{x^{n}}$,then $x^{2} \frac{d^{2} y}{d x^{2}}$ is

If $x = \int_0^y \frac{1}{\sqrt{1 + 9t^2}} dt$ and $\frac{d^2y}{dx^2} = ay$, then $a$ is equal to

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$, then $f^{\prime \prime}(-\pi)$ is equal to

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 $x^2+xy+y^2=k$, then $\frac{d^2y}{dx^2}=$

Let $P(x)$ be a polynomial of degree $2$,with $P(2)=-1, P^{\prime}(2)=0, P^{\prime \prime}(2)=2$. Then $P(1.001)$ is