If y = 3 cos(\(\frac{x}{3}\)), find \(\frac{dy}{dx}\) when x = (\(\frac{3\pi}{2}\))
A
1
B
-3
C
2
D
-1
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
y = 3cos(\(\frac{x}{3}\))
\(\frac{dy}{dx}\) = 3x(\(\frac{1}{3}\))x - sin (\(\frac{x}{3}\))
= - sin \(\frac{x}{3}\)
But x = \(\frac{3\pi}{2}\) ∴ -sin(\(\frac{x}{3}\)) = -sin(\(\frac{3\pi}{6}\))
= -sin \(\frac{(3 \times 180)}{6}\)
= - sin 90
= -1
Source: Myschool Past Questions Archive (Record #8044)