Eliminating $a$ and $b$ from the relation $y = a \log x + b$,we get $......$

$\frac{d^n}{dx^n}(e^{2x} + e^{-2x}) = $

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

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 $y^2 = p(x)$ is a polynomial of degree $3$,then $2\frac{d}{dx}\left( y^3 \frac{d^2y}{dx^2} \right)$ is equal to:

If $f(x) = 10 \cos x + (13 + 2x) \sin x$,then $f''(x) + f(x)$ is equal to