JAMB - Mathematics (2004 - No. 10)
If y = 3 cos(\(\frac{x}{3}\)), find \(\frac{dy}{dx}\) when x = (\(\frac{3π}{2}\))
1
-3
2
-1
Explanation
y = 3cos(\(\frac{x}{3}\))
\(\frac{dy}{dx}\) = 3x(\(\frac{1}{3}\))x - sin (\(\frac{x}{3}\))
= - sin \(\frac{x}{3}\)
But x = \(\frac{3π}{2}\) ∴ -sin(\(\frac{x}{3}\)) = -sin(\(\frac{3π}{6}\))
= -sin \(\frac{(3 \times 180)}{6}\)
= - sin 90
= -1
\(\frac{dy}{dx}\) = 3x(\(\frac{1}{3}\))x - sin (\(\frac{x}{3}\))
= - sin \(\frac{x}{3}\)
But x = \(\frac{3π}{2}\) ∴ -sin(\(\frac{x}{3}\)) = -sin(\(\frac{3π}{6}\))
= -sin \(\frac{(3 \times 180)}{6}\)
= - sin 90
= -1
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