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If y = x sinx, find \(\frac{dy}{dx}\)

Mathematics
JAMB 2010

If y = x sinx, find \(\frac{dy}{dx}\)

  • A. sin x - x cosx
  • B. sinx + x cosx
  • C. sinx - cosx
  • D. sinx + cosx
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Correct Answer: Option B
Explanation

If y = x sinx, then

Let u = x and v = sinx

\(\frac{du}{dx}\) = 1 and \(\frac{dv}{dx}\) = cosx

Hence by the product rule,

\(\frac{dy}{dx}\) = v \(\frac{du}{dx}\) + u\(\frac{dv}{dx}\)

= (sin x) x 1 + x cosx

= sinx + x cosx

There is an explanation video available below.


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Explanation Video

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