Find the second order derivative of the function $f(x) = x^{2} + 3x + 2$.

The $n^{th}$ derivative of $x e^x$ vanishes when

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 $f(x)$ and $g(x)$ are twice differentiable functions on $(0,3)$ satisfying $f^{\prime \prime}(x)=g^{\prime \prime}(x)$,$f^{\prime}(1)=4$,$g^{\prime}(1)=6$,$f(2)=3$,and $g(2)=9$,then $f(1)-g(1)$ is

If $y=a \cos (\log x)+b \sin (\log x)$,where $a, b$ are parameters,then $x^2 y^{\prime \prime}+x y^{\prime}$ is equal to

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