I'd probably lean towards writing it as and applying the product and chain rules.
Find g'(t).
g(t) = 3t^2/(sqrt{t^2+2t-1})
It is easier to solve by the quotient rule?
Should I separate the fraction and use the product rule?
If so, can the problem be rewritten
as 1/(sqrt{t^2+2t-1}) * 3t^2 and then apply the product rule?
What is the easiest way to find g'(t)?
I was able to find g'(t) but cannot simplify it enough to look like the book's answer.
My Answer:
g'(t) = 3t^2(-1/2)(t^2+2t-1)^(-3/2) * (2t+2) plus
(t^2+2t-1)^(-1/2) * 6t
Book's answer:
3t(t^2+3t-2) divided by (t^2+2t-1)^(3/2)
Can you simplify my answer, if correct, to look like the book's answer?