If $y=\log \left[\frac{x^2}{e^2}\right]$

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

If $y=\log \left[\frac{x^2}{e^2}\right]$ then value of $\frac{d^2 y}{d x^2}$ is:

Options:

$\frac{x^2}{e^4}$

$\frac{-2}{x^2}$

$\frac{e}{x^2}$

$2 x+\log 2$

Correct Answer:

$\frac{-2}{x^2}$

Explanation:

The correct answer is Option (2) - $\frac{-2}{x^2}$

$y=\log\frac{x^2}{e^2}=\log x^2-\log e^2$

$y=2\log x-2×1$

$\frac{dy}{dx}=\frac{z}{x}⇒\frac{d^2y}{dx^2}=\frac{-2}{x^2}$