d^n d x^n ( e^ 2x + e^ - 2x ) = - Vidyadip

MCQ

${{{d^n}} \over {d{x^n}}}({e^{2x}} + {e^{ - 2x}}) = $

A
${e^{2x}} + {( - 1)^n}{e^{ - 2x}}$
B
${2^n}({e^{2x}} - {e^{ - 2x}})$
✓
${2^n}[{e^{2x}} + {( - 1)^n}{e^{ - 2x}}]$
D
None of these

✓

Answer

Correct option: C.

${2^n}[{e^{2x}} + {( - 1)^n}{e^{ - 2x}}]$

c
(c) $\frac{d}{{dx}}[{e^{2x}} + {e^{ - 2x}}] = 2{e^{2x}} + 2{e^{ - 2x}} = {2^1}[{e^{2x}} - {e^{ - 2x}}]$

$\frac{{{d^2}}}{{d{x^2}}}[{e^{2x}} + {e^{ - 2x}}] = {2^2}[{e^{2x}} + {e^{ - 2x}}]$

$\frac{{{d^2}}}{{d{x^2}}}[{e^{2x}} + {e^{ - 2x}}] = {2^2}[{e^{2x}} - {e^{ - 2x}}]$
...................................................
...................................................
$\frac{{{d^n}}}{{d{x^n}}}[{e^{2x}} + {e^{ - 2x}}] = {2^n}[{e^{2x}} + {( - 1)^n}{e^{ - 2x}}]$.

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