Fractions and Square Roots...

Differentiate and simplify.

G(x) = square root of (3x+1/2x-1)

First, do I deal with this as a whole or break it down as two seperate functions: (3x+1) and (2x-1^1/2)

Second, I am not sure if I have written it to the correct power: 3x+1/2x-1^-1/2

-1/2(3x+1/2x-1)^-3/2