Verified answer

y = (3√x - 2)(4√x + 9)

The basic way is simply to expand the brackets/parentheses

12x -19√x - 18 = 12x - 19x^½ - 18

Then dy/dx = 12 - ½*19 x^-½ = 12 - 9.5x^-½

Well, you could do the derivative as is, using the product rule. But then there's quite a bit of simplification to be done. I would prefer to multiply out the product prior to differentiation.

y = (3√x - 2)(4√x + 9) = 12x + 27√x - 8√x - 18

  = 12x + 19√x - 18

  = 12x + 19x^½ - 18

dy/dx = 12 + 19(½)x^(-½) - 0

  = 12 + (19/2)x^(-½)