JAMB - Mathematics (2010 - No. 43)
If y = x sinx, find \(\frac{dy}{dx}\)
sin x - x cosx
sinx + x cosx
sinx - cosx
sinx + cosx
Explication
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
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