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

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

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