Question

Find the derivative of the function.
y = [(x2 + 4)/(x2 − 4)]^3

Answer 1

is it x^2 or 2x

Answer 2

\[(\frac{x ^{2}+4 }{x ^{2}-4 })^{3}\]

Answer 3

there are three ways to do this question which one did you try

Answer 4

quotient rule

Answer 5

\[3(\frac{x ^{2}+4 }{x ^{2}-4 })^{2}\]

Answer 6

So that is the derivative of the outer function. Looks good so far.
Now you multiply by the derivative of the inside?
So what'd you get for your quotient rule? :D

Answer 7

\[3(\frac{x ^{2}+4 }{x ^{2}-4 })^{2}\]*\[\frac{ (2x)(x ^{2}-4)-(x ^{2}+4)(2x) }{ (x ^{2}-4)^{2} }\]

Answer 8

is it correct?

Answer 9

yes - now you need to multiply by the earlier result

Answer 10

do i have to expand?

Answer 11

no but check if you can simplify