If $y=e^{4x} \cos 5x$,then $\frac{d^{2}y}{dx^{2}}$ at $x=0$ is

$A$ function $f$ satisfies the relation $f(x) = f''(x) + f'''(x) + \dots \infty$,where $f(x)$ is an infinitely differentiable function. If $f(1) = 5$,then the value of $f'(1) + f''(1)$ is equal to:

$\begin{aligned} & y=\sin \left(\log \left(x^2+2 x+1\right)\right) \\ & \Rightarrow(x+1)^2 \frac{d^2 y}{d x^2}+(x+1) \frac{d y}{d x}= \end{aligned}$

Find the second-order derivative of the function $f(x) = x^{3} \log x$.

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$,then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to

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