Mathematics

Find the derivative of y = sin(2x(^3) + 3x – 4)

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)
Correct Answer: Option C
Explanation

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)