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\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to

Mathematics
JAMB 1997

\(\frac{d}{dx}\) cos(3x\(^2\) - 2x) is equal to

  • A. -sin(6x - 2)
  • B. -sin(3x2 - 2x)dx
  • C. (6x - 2) sin(3x2 - 2x)
  • D. -(6x - 2)sin(3x2 - 2x)
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Correct Answer: Option D
Explanation

Let \(3x^{2} - 2x = u\)

\(y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u\)

\(\frac{\mathrm d u}{\mathrm d x} = 6x - 2\)

\(\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u\)

= \(- (6x - 2) \sin (3x^{2} - 2x)\)


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