If $y=44 x^{45}+45 x^{-44}$,then $y^{\prime \prime}=$

$A$ polynomial $P(x)$ with real coefficients has the property that $P^{\prime \prime}(x) \neq 0$ for all $x$. Suppose $P(0) = 1$ and $P^{\prime}(0) = -1$. What can you say about $P(1)$?

The maximum value of $a$ such that the second derivative of $x^4+ax^3+\frac{3x^2}{2}+1$ is positive for all real $x$ is

Let $f$ be a twice differentiable function such that $f^{\prime \prime}(x) = -f(x)$,$f^{\prime}(x) = g(x)$ and $h(x) = [f(x)]^2 + [g(x)]^2$. If $h(5) = 1$,then $h(10)$ is $\qquad$

If $y = \tan^{-1} \sqrt{\frac{1 - \cos x}{1 + \cos x}}$,then the values of $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ respectively are

If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$,then $\frac{d^2 y}{d x^2}=$