what is the answer to y ' = ½ * x^(-½) *(8x-3)^-1 + √x * [-1(8x-3)^(-2) * 8]

If you want it integrated to find y as a function of x then:

y ' = ½ * x^(-½) *(8x-3)^-1 + √x * [-1(8x-3)^(-2) * 8]

Do you want this to be integrated or what?

$$y'=0.5x^{-0.5}*(8x-3)^{-1}+\sqrt{x} *[-1(8x-3)^{-2}*8]\\\\

y'=0.5x^{-0.5}(8x-3)^{-1}+\sqrt{x}\; [-8(8x-3)^{-2}]\\\\$$

I've cleaned it up just a little bit but what do you want us to do with it?