If $y=5 \cos x-3 \sin x$,then $\frac{d^2 y}{d x^2}=$ . . . . . . .

If the function $y = \sin^{-1} x$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}$ is equal to

Let $f : S \rightarrow S$ where $S =(0, \infty)$ be a twice differentiable function such that $f(x+1) = xf(x)$. If $g : S \rightarrow R$ is defined as $g(x) = \log_{e} f(x)$,then the value of $|g''(5) - g''(1)|$ is equal to:

If $(a+bx) e^{\frac{y}{x}}=x$,then $x^3 \frac{d^2 y}{d x^2}$ is equal to

If $x=\sin \theta$ and $y=\sin^3 \theta$,then the value of $\frac{d^2 y}{dx^2}$ at $\theta=\frac{\pi}{2}$ 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 the value of $h(10)$ is