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