f(x)= (12x-18x^4+3)/(5�ã6x^2-11x^4+2)
Assuming you meant 5√ and not 5th root,
y = (12x-18x^4+3)/(5√(6x^2-11x^4+2))
Using the quotient rule,
y' = (12-72x^3)(5√(6x^2-11x^4+2)) - (12x-x^4+3)(5 / 2√(6x^2-11x^4+2))(12x-44x^3)
-------------------------------------------
25(6x^2-11x^4+2)
You can massage that if you want. See one result here:
http://www.wolframalpha.com/input/?i=derivative+%2812x-18x%5E4%2B3%29%2F%285%E2%88%9A%286x%5E2-11x%5E4%2B2%29%29