If y= ^ -1 (e^ 2 x ), then d y d x is equal to - Vidyadip

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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