JAMB - Mathematics (2000 - No. 26)
If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)
π
-π
\(\frac{π}{2}\)
-\(\frac{π}{2}\)
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
\(\frac{dy}{dx}\) = 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
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