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