JAMB 1997 · UME · Q38

Differentiate $\dfrac{6x^3 - 5x^2 + 1}{3x^2}$ with respect to $x$ .

Worked solution (try it first)

Divide each term by $3x^2$ first: $y = 2x - \frac53 + \frac13x^{-2}$ .
Differentiate term by term: $2x$ gives 2, the constant gives 0, and $\frac13x^{-2}$ gives $-\frac23x^{-3}$ .
So $\frac{dy}{dx} = 2 - \frac{2}{3x^3}$ , option C.