Differentiate :(i) `xe^(x)` , (ii) `x^(2)e^(x) sin x`

Explanation

(i) `d/(dx) (xe^(x)) =x, d/(dx) (e^(x)) (x) = (xe^(x) +e^(x).1) = e^(x) (x+1) `
(ii) ` d/(dx) (x^(2)e^(x) sin x) = d/(dx) [(x^(2)e^(x))sin x]`
` = (x^(2)e^(x)) .d/(dx) (sin x) + sin x . d/(dx) (x^(2)e^(x))`
` = x^(2)e6(x) cos x + sin x.{ x^(2).d/(dx) (e^(x)) +e^(x).d/(dx)(x^(2))}`
` = x^(2)e^(x) cos x + sin x .[x^(2)e^(x) + 2xe^(x)]`
` x^(2)e^(x) cos x + x^(2)e^(x) sin x + xe^(x) sin x `
` = xe^(x) [ x cos x + x sin x + 2 sin x]`