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If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)

Mathematics
JAMB 2000

If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)

  • A. π
  • B.
  • C. \(\frac{π}{2}\)
  • D. -\(\frac{π}{2}\)
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Correct Answer: Option B
Explanation

y = 2x cos2x - sin2x
\(\frac{dy}{dx}\) = 2 cos2x +(-2x. 2sin2x) - 2cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x 2sin2x
= -4 x (\(\frac{π}{4}\)) sin2 x (\(\frac{π}{4}\))
= -(π) x 1 = - π

There is an explanation video available below.


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Explanation Video

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