CUET Mathematics 2025 14 May Shift 1 PYQs

If $f(x) = x^3\log_e x$, Then $f''(e^2)$ is equal to

$f(x)=\begin{cases}\dfrac{|x|}{x},&x\ne0\\1,&x=0\end{cases}$

$g(x)=\begin{cases}x\sin\left(\dfrac{1}{x}\right),&x\ne0\\0,&x=0\end{cases}$

Then at the origin, which one of the following is true?

If $y = 5e^{2x} + 4e^{3x}$, then $\frac{d^2y}{dx^2}$ equals: