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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $y=\log _e\left(\frac{x^2}{e^2}\right)$, then $\frac{d^2 y}{d x^2}$ equals
  • A
    $-\frac{1}{x}$
  • B
    $-\frac{1}{x^2}$
  • C
    $\frac{2}{x^2}$
  • ✓
    $-\frac{2}{x^2}$
✓

Answer

Correct option: D.
$-\frac{2}{x^2}$
We have,  $y=\log _e\left(\frac{x^2}{e^2}\right)$
$\therefore \frac{d y}{d x}=\frac{e^2}{x^2} \cdot \frac{1}{e^2} \cdot 2 x=\frac{2}{x} $
$\Rightarrow \frac{d^2 y}{d x^2}=-\frac{2}{x^2}$

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