Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x
A
\(\frac{2 + 2}{3x^3}\)
B
2 + \(\frac{1}{6x}\)
C
2 - \(\frac{2}{3x^3}\)
D
\(\frac{1}{5}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{6x^3 - 5x^2 + 1}{3x^2}\)
let y = 3x2
y = \(\frac{6x^3}{3x^2}\) - \(\frac{6x^2}{3x^2}\) + \(\frac{1}{3x^2}\)
Y = 2x - \(\frac{5}{3}\) + \(\frac{1}{3x^2}\)
\(\frac{dy}{dx}\) = 2 + \(\frac{1}{3}\)(-2)x-3
= 2 - \(\frac{2}{3x^3}\)
Source: Myschool Past Questions Archive (Record #30852)