Let's see:

you would actually use product rule with chain rule(for this (3x+1)^(3/2)), so we will have -

f'(x) = ((3x+1)^(3/2))' * (2x+4) + ((3x+1)^(3/2))*(2x+4)' =

(3/2)*(3x+1)^(1/2) *(3)*(2x+4) + ((3x+1)^(3/2))*(2x) =

3(3x+1)^(1/2) *(2x+4) + ((3x+1)^(3/2))*(2x) =...

would you need any help further to factorize or you are ok?