Differentiation Question 353
Question: $ \frac{d^{n}}{dx^{n}}(e^{2x}+{e^{-2x}})= $
Options:
A) $ e^{2x}+{{(-1)}^{n}}{e^{-2x}} $
B) $ 2^{n}(e^{2x}-{e^{-2x}}) $
C) $ 2^{n}[e^{2x}+{{(-1)}^{n}}{e^{-2x}}] $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{d}{dx}[e^{2x}+{e^{-2x}}]=2e^{2x}+2{e^{-2x}}=2^{1}[e^{2x}-{e^{-2x}}] $
$ \frac{d^{2}}{dx^{2}}[e^{2x}+{e^{-2x}}]=2^{2}[e^{2x}+{e^{-2x}}] $
$ \frac{d^{2}}{dx^{2}}[e^{2x}+{e^{-2x}}]=2^{2}[e^{2x}-{e^{-2x}}] $
…………………………………………… …………………………………………… $ \frac{d^{n}}{dx^{n}}[e^{2x}+{e^{-2x}}]=2^{n}[e^{2x}+{{(-1)}^{n}}{e^{-2x}}] $ .
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