If y = (1 - 2x)\(^3\), find the value of dy/dx at x = -1
A
57
B
27
C
-6
D
-54
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
y = (1 - 2x)\(^3\)
let u = 1-2x
du/dx = -2
∴y = u\(^3\)
dy/du = 3u\(^2\)
But dy/dx = du/dx * dy/du
= -2 * 3u\(^2\)
= -6u\(^2\)
= -6(1-2x)\(^2\)
At x = -1: dy/dx = -6(1 - 2(-1))\(^2\)
dy/dx = -6(1 + 2)\(^2\)
= -6 * 3\(^2\)
= -6 * 9
= -54
Source: Myschool Past Questions Archive (Record #8478)