Question

can someone help me on the attachment and not go to wolfframealpha to show me how to work it

Answer 1

\[f(x)=(x^2-2)/\sqrt{x^2-1}\]
quotient rule would be a pain here so let's rewrite this as a product of two functions:
\[f(x)=(x^2-2)/\sqrt{x^2-1}=(x^2-2)(x^2-1)^(-1/2)\]
that's (x^2-1)^(-1/2) on the right there...
product rule (fg)'=f'g+g'f

Answer 2

ok

Answer 3

\[f'(x)=2x(x^2-1)^(-1/2)-(x^2-2)(1/2)(x^2-1)^(-3/2)(2x)\]
\[=2x/\sqrt{x^2-1}-(x^3-2x)/\sqrt{(x^2-1)^3}\]
simplify

Answer 4

but that not one of the answer choices here a list

Answer 5

the first answer choice is on the first attachment where its show the problem