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Differentiation (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Differentiation (p-1)1 Mark
MCQ
If $y =\log \left(\frac{e^x}{x^2}\right)$ then $\frac{d y}{d x}=$ ?
  • A
    $\frac{2-x}{x}$
  • ✓
    $\frac{x-2}{x}$
  • C
    $\frac{e-x}{e x}$
  • D
    $\frac{x-e}{e x}$
✓

Answer

Correct option: B.
$\frac{x-2}{x}$
(b) $\frac{x-2}{x}$
Hint:
$
\begin{aligned}
y & =\log \left(\frac{e^x}{x^2}\right)=\log e^x=\log x^2 \\
& =x-2 \log x \quad \ldots[\because \log e=1]
\end{aligned}
$
$\therefore \frac{d y}{d x}=1-\frac{2}{x}=\frac{x-2}{x}$

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