Question

Y=(3x-2)/(sqrt(2x+1)) differentiate

I have the quotient rule set up but I'm having trouble simplifying

Answer 1

`y=(3x-2)/(√(2x+1))=(3x-2)/((2x+1)^(1/2))`

The quotient rule gives


`y'=((2x+1)^(1/2)(3x-2)'-(3x-2)\left((2x+1)^(1/2)\right)')/(\left((2x+1)^(1/2)\right)^2)=(3(2x+1)^(1/2)-(2(3x-2))/(2(2x+1)^(1/2)))/(2x+1)`

Factor out
`(2x+1)^(-1/2)` to get


`((2x+1)^(-1/2)\left(3(2x+1)^(2/2)-(3x-2)\right))/(2x+1)=(6x+3-6x+2)/((2x+1)^(3/2))=(3x+5)/((2x+1)^(3/2))`