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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
If $y=\log _e\left(\frac{x^2}{e^2}\right)$, then $\frac{d^2 y}{d x^2}$ equals
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Answer

$\text { 84. (d) : We have, } y=\log _e\left(\frac{x^2}{e^2}\right)$
$\therefore \frac{d y}{d x}=\frac{e^2}{x^2} \cdot \frac{1}{e^2} \cdot 2 x=\frac{2}{x}$
$\Rightarrow \frac{d^2 y}{d x^2}=-\frac{2}{x^2}$

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