Differentiate \((2x+5)^{2} (x-4)\) with respect to x.
A
4(2x+5)(x-4)
B
4(2x+5)(4x-3)
C
(2x+5)(2x-13)
D
(2x+5)(6x-11)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(y = (2x + 5)^{2} (x - 4)\)
\(\frac{\mathrm d y}{\mathrm d x} = (2x + 5)^{2} (1) + (x - 4)(2)(2)(2x + 5)\)
= \((2x + 5)(2x + 5 + 4x - 16)\)
= \((2x + 5)(6x - 11)\)
Source: Myschool Past Questions Archive (Record #2128)