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

Mathematics

JAMB 2005

A. cos (2x³ + 3x - 4)
B. -cos (2x³ + 3x - 4)
C. (6x² + 3) cos (2x³ + 3x - 4)
D. -(6x² + 3) cos (2x³ + 3x - 4)

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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)

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

Correct Answer: Option C

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