Expert: Paul Klarreich - 11/9/2011

Question
Derivative of -48x/(x^2+12)^2. I factor out -48*(x/(x^2+12)^2 then get (x^2+12)^2*1-4x^2(x^2+12)/(x^2+12)^4 factor out (x^2+12) and end up with (x^2+12)^2-4x^2/(x^2+12)^3 and don't know where to go from here. I multiplied out the (x^2+12)^2 and ended up with the wrong answer. Please help.
Thank You

Answer
Questioner: Andrea
Country: Nebraska, United States
Category: Calculus
Private: No
Subject: Calculus
Question: Derivative of -48x/(x^2+12)^2. I factor out -48*(x/(x^2+12)^2 then get (x^2+12)^2*1-4x^2(x^2+12)/(x^2+12)^4 factor out (x^2+12) and end up with (x^2+12)^2-4x^2/(x^2+12)^3 and don't know where to go from here. I multiplied out the (x^2+12)^2 and ended up with the wrong answer. Please help.
Thank You
...................................
Wow! What a mess!  Anyway:

Yes, take out the -48; we don't need it now.
       x
y = -------------
   (x^2 + 12)^2

Quotient rule:  (and power law, too)

    (x^2 + 12)^2(1) - 2(x^2 + 12)(2x)(x)
y' = ------------------------------------
         (x^2 + 12)^4  <<<  Yes: ()^2^2 = ()^4


    (x^2 + 12)^1(1) - 2(2x)(x)
y' = --------------------------------  << cancel one factor of (x^2 + 12)
         (x^2 + 12)^3

CANCEL FROM BOTH TERMS ON TOP -- I THINK THAT IS WHERE YOU WENT WRONG.

    x^2 + 12 - 4x^2
y' = -----------------
     (x^2 + 12)^3

etc.
------------------------------------------------------------
Note:  This may help, now and then:

http://www.calculator-grapher.com/derivative-calculator.html

although in this case it won't do the simplification for yuo.

NEXT MONTH, you will want:

http://integrals.wolfram.com/index.jsp

THAT one is very good -- it does integrals.