The $n^{th}$ derivative of $x^{n + 1}$ is

If $y=2 \sin x+3 \cos x$ and $y+A \frac{d^2 y}{d x^2}=B$,then the values of $A$ and $B$ are respectively:

If $f(x) = \frac{x^2}{x+a}$,then $f^{\prime \prime}(a)$ is equal to

Let $f$ and $g$ be twice differentiable functions such that $f(x) \cdot g(x) = 1$ for all $x \in R$ and $f'$ and $g'$ are never zero. Then $\frac{f''(x)}{f(x)} + \frac{g''(x)}{g(x)}$ equals:

If $y=3 e^{5 x}+5 e^{3 x}$,then $\frac{d^{2} y}{d x^{2}}-8 \frac{d y}{d x}=$ (in $y$)

If $f$ is twice differentiable such that $f''(x) = -f(x)$,$f'(x) = g(x)$,$h'(x) = [f(x)]^2 + [g(x)]^2$,and $h(0) = 2$,$h(1) = 4$,then the equation $y = h(x)$ represents: