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