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