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

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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

${d \over {dx}}\{ \log (\sec x + \tan x)\} = $

If a = b then ax = ...........

b + x
bx
b - x
b ÷ x

If the function $f(x)=\frac{\cos (\sin x)-\cos x}{x^{4}}$ is continuous at each point in its domain and $f (0)=\frac{1}{ k },$ then $k$ is ........

Let f(x) = |x| and g(x) = |x³|, then:

f(x) and g(x) both are continuous at x = 0
f(x) and g(x) both are differentiable at x = 0
f(x) is differentiable but g(x) is not differentiable at x = 0
f(x) and g(x) both are not differentiable at x = 0

The magnitude of the vector 6i + 2j + 3k is equal to:

5
1
7
12

Let $R$ be the set of real numbers and $f: R \rightarrow R$ be defined by $f(x)=\frac{\{x\}}{1+[x]^2}$, where $[x]$ is the greatest integer less than or equal to $x$, and $\left\{x{\}}=x-[x]\right.$. Which of the following statements are true?

$I.$ The range of $f$ is a closed interval.

$II.$ $f$ is continuous on $R$.

$III.$ $f$ is one-one on $R$

If $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\{ - 2}&3&{ - 1}\\3&1&2\end{array}} \right]$and $I $is a unit matrix of ${3^{rd}}$order, then $({A^2} + 9I)$ equals

Let $f$ be continuous on $[1, 5]$ and differentiable in $(1, 5).$ If $f(1)=-3$ and $f'(x) \ge 9$ for all $x \in (1,\;5)$, then

$\int_{}^{} {\frac{{2x{{\tan }^{ - 1}}{x^2}}}{{1 + {x^4}}}} \;dx = $

If $f:R \to R$, then $f(x) = \;|x|$ is