Find the derivative of y = sin(2x\(^3\) + 3x - 4)
A
cos (2x3 + 3x - 4)
B
-cos (2x3 + 3x - 4)
C
(6x2 + 3) cos (2x3 + 3x - 4)
D
-(6x2 + 3) cos (2x3 + 3x - 4)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
y = sin (2x\(^3\) + 3x - 4)
let u = 2x\(^3\) + 3x - 4
∴du/dx = 6x\(^2\)
y = sin u
dy/du = cos u
dy/dx = du/dx * dy/du
∴dy/dx = (6x\(^2\) + 3) cos u
= (6x\(^2\) + 3)cos(2x\(^3\) + 3x - 4)
Source: Myschool Past Questions Archive (Record #8483)