Find \(\frac{dy}{dx}\), if y = \(\frac{2}{3}\) x\(^3\) - \(\frac{4}{x}\)
A
3x2 - \(\frac{4}{x}\)
B
2x2 +\(\frac{4}{x^2}\)
C
3x2 + \(\frac{4}{x^2}\)
D
2x2 - \(\frac{4}{x}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
y = \(\frac{2}{3}\)x\(^3\) - \(\frac{4}{x}\)
\(\frac{dy}{dx}\) = 2x\(^2\) - (-4)x\(^{-2}\) = 2x\(^2\) + \(\frac{4}{x^2}\)
Source: Myschool Past Questions Archive (Record #44832)