If $y = log_e \left(\frac{x^3}{e^3}\right),$ then $\frac{d^2y}{dx^2} $ is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-\frac{3}{x^2}$
$y=\log_e\left(\frac{x^3}{e^3}\right)$ [Given]
$\frac{dy}{dx}=\frac{e^3}{x^3}×\frac{3x^2}{e^3}=\frac{3}{x}$
$⇒\frac{d^2y}{dx^2}=-\frac{3}{x^2}$