If $y=\log \left(\frac{x^5}{e^5}\right)$, then $\frac{d^2 y}{dx^2}$ is,
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) - $\frac{-5}{x^2}$
$y = \log\left(\frac{x^5}{e^5}\right)$
$= \log x^5 - \log e^5$
$= 5\log x - 5$
$\frac{dy}{dx} = \frac{5}{x}$
$\frac{d^2 y}{dx^2} = -\frac{5}{x^2}$
$\frac{d^2 y}{dx^2} = -\frac{5}{x^2}$