`a)`

`y=x^3+2x^2-4x+1`

`-> y'=(x^3)'+(2x^2)'-(4x)'+1'`

`-> y'=3x^2+4x-4`

`b)`

`y=xsqrtx`

`-> y=x*x^[1/2]`

`-> y=x^[3/2]`

`-> y'=3/2x^[1/2]`

`c)`

`y=[x^2+1]/[3x+2]`

`-> y'=[(x^2+1)'(3x+2)-(3x+2)'(x^2+1)]/[(3x+2)^2]`

`-> y'=[2x(3x+2)-3(x^2+1)]/[(3x+2)^2]`

`-> y'=[6x^2+4x-3x^2-3]/[(3x+2)^2]`

`-> y'=[3x^2+4x-3]/[(3x+2)^2]`

`d)`

`y=[2sqrtx]/[x+1]`

`-> y'=[(2sqrtx)'(x+1)-(x+1)'(2sqrtx)]/[(x+1)^2]`

`-> y'=[x^[-1/2] (x+1)-2sqrtx]/[(x+1)^2]`

`-> y'=[x^[1/2]+x^[-1/2]-2x^[1/2]]/[(x+1)^2]`

`-> y'=[-x^[1/2]+x^[-1/2]]/[(x+1)^2]`