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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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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