Differentiate with respect to X
(i) `y=xlnx " "` (ii) `y=x^(2)e^(x) " "`(iii) `y=(sin x)/(x) " "` (iv) `y=(3x^(2)+2sqrt(x))/(x)`

Explanation

(i) `(dy)/(dx)=x((1)/(2))+lnx=1+lnx " "` (ii) `(dy)/(dx)=2xe^(2)e^(x)+x^(2)e^(x)=xe^(x)(2+x)`
(iii) `y=x^(-1)sinx`
`(dy)/(dx)=(-x^(-2))sinx+x^(-1)cosx`
(iv) `y=3x+2x^(-1//2)`
`(dy)/(dx)=3+2(-½ x^(-3//2))=3-x^(-3//2)`