If y = e^ 2x + e^ - 2x e^ 2x - e^ - 2x , then dy dx = - Vidyadip

MCQ

If $y = {{{e^{2x}} + {e^{ - 2x}}} \over {{e^{2x}} - {e^{ - 2x}}}}$, then ${{dy} \over {dx}} = $

✓
${{ - 8} \over {{{({e^{2x}} - {e^{ - 2x}})}^2}}}$
B
${8 \over {{{({e^{2x}} - {e^{ - 2x}})}^2}}}$
C
${{ - 4} \over {{{({e^{2x}} - {e^{ - 2x}})}^2}}}$
D
${4 \over {{{({e^{2x}} - {e^{ - 2x}})}^2}}}$

✓

Answer

Correct option: A.

${{ - 8} \over {{{({e^{2x}} - {e^{ - 2x}})}^2}}}$

a
(a) $y = \frac{{{e^{2x}} + {e^{ - 2x}}}}{{{e^{2x}} - {e^{ - 2x}}}}$

$\therefore \frac{{dy}}{{dx}} = \frac{{({e^{2x}} - {e^{ - 2x}})2({e^{2x}} - {e^{ - 2x}}) - ({e^{2x}} + {e^{ - 2x}})2({e^{2x}} + {e^{ - 2x}})}}{{{{({e^{2x}} - {e^{ - 2x}})}^2}}}$

$ = \frac{{ - 8}}{{{{({e^{2x}} - {e^{ - 2x}})}^2}}}$.

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