NECO 2023 · Paper 1 · Q15

Differentiate $\left(\dfrac{2 + y}{y}\right)^2$ with respect to $y$ .

Worked solution (try it first)

Simplify first: $\dfrac{2 + y}{y} = 1 + \dfrac2y$ , so the expression is $\left(1 + \dfrac2y\right)^2 = 1 + \dfrac4y + \dfrac{4}{y^2}$ .
Write it as powers of $y$ : $1 + 4y^{-1} + 4y^{-2}$ .
Differentiate each term (multiply by the power, then take 1 off it): $-4y^{-2} - 8y^{-3}$ .
So the derivative is $-\dfrac{4}{y^2} - \dfrac{8}{y^3}$ , option D.