Do I just multply out the top to get f(x) and then get the derivative by the quotient rule from there?
I got what I thought was the derivative: (12x^2(X^2+2)-(3x^2-3)(x^2-2)(2x))/(x^2+2)^2 but it said I was incorrect.
You seem to have forgotten a "/"! Did you mean (x^2+ 2)(3x^2- 3)/(x^2- 2)?
(You also seem to have forgotten the parentheses around x^2+ 2. Or did you really mean "x^2+ [2(3x^2- 3)]= x^2+ 6x^2- 6= 7x^2- 6 as you wrote?)
By the quotient rule, the derivative is [((x^2+2)(3x^2- 3))'(x^2- 2)- (x^2+2)(3x^2-3)(x^2- 2)']/(x^2-2)^2.
You can do the derivative of the numertor, ((x^2+2)(3x^2- 3))' either by first multiplying it out or by using the product rule.
Break it down. You have . Write out the functions and . Then find the derivatives and . Write them here for us to check, and we can figure out where you might be going wrong. From your answer in your first post, it appears you think the derivative of is . Is that the case?
Ive tried everything I got u'(x) to equal 12x^3-18x. So I did the quotient rule: (36x^2-18)(x^2+2)-2x(12x^3-18x) all over (x^2+2)^2. I've tried foiling and product rule on (36x^2-18)(x^2+2) but I still ended up with the wrong anser and its EXTREMELY frustrating!!!
You'll feel better when you realise that you've made errors, which is more reassuring than if the maths weren't capable of behaving itself! So re-read the given solutions. Here's another:
... where (key in spoiler) ...
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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