If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{4}\)
A
π
B
-π
C
\(\frac{π}{2}\)
D
-\(\frac{π}{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
y = 2x cos2x - sin2x
\(\frac{dy}{dx}\) = 2 cos2x +(-2x. 2sin2x) - 2cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x 2sin2x
= -4 x (\(\frac{\pi}{4}\)) sin2 x (\(\frac{\pi}{4}\))
= -(\pi) x 1 = - \pi
Source: Myschool Past Questions Archive (Record #833)