If $y=\log _e\left(\frac{x^4}{e^4}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $-\frac{4}{x^2}$
$y=\log\left(\frac{x^4}{e^4}\right)$
$= \log x^4 - \log e^4 = 4\log x - 4$
$\frac{dy}{dx}=\frac{4}{x}$
$\frac{d^2y}{dx^2}=-\frac{4}{x^2}$
$\frac{d^2y}{dx^2}=-\frac{4}{x^2}$