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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
Derivative of $e^{2 x}$ with respect to $e^x$, is
  • A
    $e^x$
  • B
    $2 e^x$
  • C
    $2 e^{2 x}$
  • D
    $2 e^{3 x}$
✓

Answer

Let $u=e^{2 x}$ and $v=e^x$
$
\Rightarrow \quad \frac{d u}{d x}=2 e^{2 x}, \frac{d v}{d x}=e^x \therefore \quad \frac{d u}{d v}=\frac{d u / d x}{d v / d x}=\frac{2 e^{2 x}}{e^x}=2 e^x
$

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