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

If $a \neq b, x \neq n \pi, n \in Z$ and $y^2 = a^2 \cos^2 x + b^2 \sin^2 x$,then $\frac{d^2 y}{dx^2} + y =$

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$, then $\left(1+a^2 x^2\right)y''+2 a^2 x y'$ is equal to

If $x^m + y^m = k$ where $(m \neq 1)$ and $\frac{d^2y}{dx^2} = \frac{ax^b}{y^c}$ such that $a + b + c = 0$, then the value of $k$ is...

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:

If $f(x) = \sin x + \cos x$, then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to