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

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

If y = x sinx, find (frac{dy}{dx})
  • A.
    sin x – x cosx
  • B.
    sinx + x cosx
  • C.
    sinx – cosx
  • D.
    sinx + cosx
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

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