"What is the derivative of (3x)/(2x^2-18)?"
Let u = 3x and v = (2x2-18)-1
Use the chain rule: duv/dx = udv/dx + vdu/dx:
du/dx = 3 dvdx = -(2x2-18)-24x
d(3x(2x2-18)-1)/dx = -12x2(2x2-18)-2 + 3(2x2-18)-1
or (3(2x2-18) - 12x2)/(2x2-18)2 → -(6x2 + 54)/(2x2-18)2 → -(3/2)(x2 + 9)/(x2 - 9)2