To take the derivative of a fraction, use the Quotient Rule. Low d high minus high d low/square the bottom and off you go is the nemonic that my teacher taught. (x^2+2)(0)- (3)(2x)/(x^2+2)^2. Remember to use product rule for x^2 and that the derivative of any constant is 0.
So, the final answer is:
-6x/(x^2+2)^2