JAMB 2001 · UME · Q33

Differentiate $(2x + 5)^2(x - 4)$ with respect to $x$ .

Worked solution (try it first)

Product rule with $u = (2x + 5)^2$ and $v = x - 4$ .
By the chain rule, $u' = 2(2x + 5) \times 2 = 4(2x + 5)$ , and $v' = 1$ .
So $\frac{dy}{dx} = 4(2x + 5)(x - 4) + (2x + 5)^2$ .
Take out the common factor $2x + 5$ : $(2x + 5)(4x - 16 + 2x + 5) = (2x + 5)(6x - 11)$ , option A.