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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $y=\tan ^{-1}\left(e^{2 x}\right)$, then $\frac{d y}{d x}$ is equal to
  • A
    $\frac{2 e^{2 x}}{1+e^{4 x}}$
  • B
    $\frac{1}{1+e^{4 x}}$
  • C
    $\frac{2}{e^{2 x}+e^{-2 x}}$
  • D
    $\frac{1}{e^{2 x}-e^{-2 x}}$
✓

Answer

Given, $y=\tan ^{-1}\left(e^{2 x}\right)$
\[\therefore \frac{d y}{d x}=\frac{1}{1+e^{4 x}} \times 2 e^{2 x}=\frac{2 e^{2 x}}{1+e^{4 x}}\]

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